Math Forum - Problem of the Week Submissions for Canadian Soccer Student Short Answer Long Answer Student 1 Each players run 1.68 kilometers. When the players start and go to the first point they run 100 meters. I relised that because in the feild was a right triangle. The right triangle is 1,3, and to 2. 5 to 3 is 120. Half of that is 60. Also 3 to 2 already says it is 80 meters long. Then I used the Pythagorem Thearom to find the hypotenuse of the right triangle. With the work I did the Hypotenuse is 100 meters long. So 1 to 2 is 100m and so start to 1. Then I calculated how long they ran and they ran 560 meters. But they ran around 3 times. Then I times 560*3=1680m. Then to turn my answer to km I knew 1000m=1km. Which then my answer was 1.68. Student 2 The answer for this problem I got is 144.2 by using a scientific term. Directions: s= squared Dear To Whom It May Concern, I thought that the problem was kind of easy because my science already taught us the equation to use for this but I’m not sure if I got the answer correct. Anyways I tried to do it but first I asked myself the question,” How much piece of information do I have in order to complete this problem?" So I went on to collect the info. And I got this: • To find the answer I need to use Pythagorean Theorem equation, which is A2+B2=C2 (the 2 stands for the square). • I also now that field’s length is 120 meters and the width of 80 meters. • Also during the practice session the players run the Double V three times. • Before the players run, they start their race at the southwest corner of t he field, run to the top diagonal line, then go to the southeast corner completing the first V and ht second V takes them to the bottom of the center line and the non to the northwest corner, finishing that off by sprinting back to the southwest corner. © 1994-2016 Drexel University http://mathforum.org/pows/ Page 1 of 14 ~ So now I know my facts of the problem. So I go on and try to figure out the problem. I know the Pythagorean Theorem equation, which is A2+B2=C2 (the 2 stands for the square). I take a piece of paper and set my problem: • As+Bs=Cs I then fill in the numbers for the second step. • 120s +80s=Cs I got the second step done so I move on to the other step. The next step I figure out the number which was squared by the equation. • • • 120s = 14,400 80s = 6,400 14,400 + 6,400 = Cs I did that step but the step after that is very important because if you don’t get the addition rite than you won’t come up with the right answer. • • 14,400 + 6,400 = 20,800 20,800 = Cs Now I did all the steps but I only have one most important step left that is to square root the answer I got for the addition. Student 3 i don't have a solution. Student 4 i did not come up with a solution I dont have a answer Student 5 © 1994-2016 Drexel University http://mathforum.org/pows/ • Cs = 144.2 I got the answer of 144.2 by doing these steps and I hope I get it right. This was kind of fun also because I got to learn new stuff and I am aslo very into sports. i did not understand this problem. so therefore i didn't do the problem. so i do not have an answer. i did not understand this problem of the week. I didn't get this problem so I dont have an answer Page 2 of 14 Student 6 Student 7 Student 8 I use the pythagorean theorem a2+b2=c2 which equals 10,000 but I forgot to square and add it together I entered the problem by multiplying the length and the width of the soccer feild and then i divided the sides of the field. ? i multiplied 60*60 then i multiplied 80*80 then added it together and got 10,000 then i squared it and got 100 so i knew that the diagonal eqaled 100 so since it was 4 lines going diagnol i multiplied 4 times 100 and since it was 2 80 lines i multiplied 80 by 2 and added 160 and 400 120+80/4x4 in the problem it says the length of the whole field was 120 and the width 80. Since they run from a corner of the field to the center, i divided 120 by 2 which is 60. i then multiplyed 60x60 (A squared) and 80x80 (B squared) then added them to find the length they ran (C squared) i came to: 60x60=3600 80x80=6400 3600+6400=10000 Student 9 1.68 Student 10 Student 12 what I did was I i mulltiplied to the second power The answer that i came up with is 1.68 kilometers. 16.8 Student 13 16.8 Student 14 Each player will run a distance of 1.68 Student 11 © 1994-2016 Drexel University http://mathforum.org/pows/ now this is as far as i could get. im pretty sure i have to find the square root of 10000 and then multiply that times 4 (the lines they ran) + 80 + 80 (the two sides they ran)= the full length they ran. I multiplied 60 times 2 and and then times 8. 1.68 I got the answer by dividing the 80 meters by how times they went around the triangles. i got that answer by multiplying and divdceding and i use the forlum and thats how i got the answer 16.8 i got that answer by multiplying and divdceding and i use the forlum and thats how i got the answer 16.8 The first thing I did to get my answer was, didvide the 80 kilometers by how many times they went around each triangle. Page 3 of 14 Student 15 Student 16 Student 17 kilometers. 1.68 km is my answer for the Canadian Soccer 1.68 km is my final answer for Canadian Soccer. My answer came out to be 13.3 kilometers each player runs. Student 18 14.4 c2 Student 19 For my final solution I got 0.432 Student 20 The answer to the problem of the week for Canadian Soccer is 144.2 I forget how I got the answer, but on the paper the answer was on the paper. The answer is 1..68km. I just multiplied a exponent 2 and b exponent 2 and multiplied it with the number 120 and 80. I got 1.68. I think i got the right answer. .first i drew the pythagorean then i wrote down the information i know like how the length is 120 meters and the width is 80 meters. .Next i tried to figure out the direction of the double v run so i follow the double v.then i muliplyed 120 times 80 which equals 9600 divide that in to 2 and get 4800 divided that in to 3 to get 1600 =400/5=80/ 6=13.3 So my answer would be 13.3 kilometers each plaqyer will run I used the Pythagorean theoren a2+b2+=c2 then i took 120 meters and made it 120 to the secound power and did the same to 80 and made it 80 to the secound power .Then i add 120to the secound power and 80 to the secound power=c2. Then i got 14,400+6,400 and that = c2. then when you add them together you get 20,800k=c2. So c2 divided 144 and divided that by 2 = 14.4=c2. its the length of the triangle that has one leg equal. First I did 120 squared + 80 squared and then I mulitplied 120 times 120 and 80 times 80 and then I got 14400+6400. Then I added those two together and I got 20800 and I got that I had to figure out the square root of 20800 and I got 144.2 and I rounded it to 144. After that I mulitiplied 144 times 3 because in the problem it said that they ran the Double V 3 times. So after I multiplied those two numbers I got 432 and then I divided it by 1000 because there is 1000 meters in each kilometer, and then that's how I got my answer of 0.432. I understand that the students have to run a Double V Pattern, and the feild is120 meters in length and 80 meters in width. I didn't understand why thay wanted us to use a diagram to solve the problem instead of using the pythagorean theorem At first I thought I wouldn't use the diagram . I solved the problem by using the © 1994-2016 Drexel University http://mathforum.org/pows/ Page 4 of 14 Student 21 each player runs 0.432 kilometers. Student 22 For my answer I got 3.1200 Student 23 the answer we got is 1.68kilometers per person we rounded it to 2 kilometers. pythagorean theorem. I used a square as 120 and b square as 80 and I got c square as 144.2. first i took the pythagorean theorem a squared plus b squared equals c squared. a equals 120 to the second power and equals 14400. b equals 80 to the second power anmd equals 6400. i added both them both together and got 20,800. then i found the sqAURE root of 20,800 and got 144.2. then I rounded it and got 144. then i mulitipled 144 by 3 and got 432. i times it by 3 because of the # of times they went around the the double v. then i divied 432 into a 1000.i dived it into 1ooo becuase 1000 eqUALS ONE KILOMETER.then i got 0.432.so each player runs 0.432 kilometers. First I took 120 to the second power and I got 14400 And then I put 80 to the second power and I got 6400 theen I took 14400 add it to 6400 then my answer came out to 20800 then I took the number and the divded the two into it and got the answer 3.1200 what is the question: how many kilometers did each player run. what we know: we know that the field has the lengtth of 120 meters and the width of 80 meters. what we did: We used the pythagorean theorem. we divided 120 by 2 we got the answer 60 we divided since they only went half way up. so what we did is this: 60^2+80^2=diag. so 60 ^2 = 3600 and 80 ^2 =6400 next we added them both.3600+6400=10,000. next we wanted to find the square root of 10,000 we got 100. for every time they went diagonaly it was 100 meters.every time they went up or down it was 80 meters. so they went : they went up 100 meters diagonaly, they went down 100 meters diagonaly they went straight up 80 meters they went back down 100 meters diagonaly then they went back up 100 meters diagonaly then they went down 80 meters again. in total they went 560 meters. since they went around three times we multiplied it by 3 which we got the answer of 1,680. since we know that 1,000 meters equal 1 kilometer we divided. 1,680 divided by 1,000 equals 1.68 kilometers we rounded the answer to 2 kilomters. Our answer: we rounded it to 2 kilometers. © 1994-2016 Drexel University http://mathforum.org/pows/ Page 5 of 14 Student 24 Each player will run 0.432 kilometers three times around the Double V. Student 25 the pattern is that their running a V every other time then finishing at the center to the opposite to where they started Each player will run 1.68 kilometers. Student 26 Student 27 Each player will run 1.68 kilometers. © 1994-2016 Drexel University http://mathforum.org/pows/ First you have to know the equation you are useing. I used the Pythagirean theorem- A square+ B square + c square. So then I looked at the information I had and i can up wit 120 to the secound power + 80 to the seound power = c square. Then i multiply 12 times 12 and got 14400. Then 80 times 80 and it equaled 6400. i added them up and i got 20800= C square. Then i found the Square route of 20800 and I got 144.2. I rounded it off to 144. So now I have c square =144. I Mulitplied 144 times 3 because 3 is how many times one player ran around the Double V. And I got 432. So the I divided it to 1000 because 1000= 1 kilometer. And I got 0.432. So my answer is 432 kilometers for each player running 3 times around the Double V. a2+b2=c2 120+80=c2 240+160=c2 400=c2 c2=800 First I saw that the field was divided into two to form two congruent right triangles. I also saw that the first path travelled along the hypotenuse of that trinagle. So I used the Pythagorean Theoreum to find its length; doing this would find part of the distance of the run. 120 / 2 = 60 and using the Pythagorean Theoreum, 3600 + 8400 = 10000. The square root of this is 100, so the distance from the southwestern corner to the northern middle point is 100 m and since the run travelled then down to the southeastern corner, I added another 100 m because the trinagles are congruent. I added another 160 m for the times when the path ran along the width twice. And then there was a repeat of the first paths, the ones that ran along the hypotenuse, so I added another 200 m for a total of 560 m. I multiplied this by 3 because they players ran this pattern 3 times; the product came out as 1680 m. And because there are 1000 m in 1 km, I divided 560 by 1000 to get 1.68 km. I first drew a diagram of the soccer field entering all measuremnts (80m on side, 120m on bottom, ect.). I then drew the path in pen to not get confused on what was the path and what wasn't. I took the two sides (80m each) and added them together to get part of the length with 160m. I then needed to find the length of the hypotenuse of the triangles that were drawn. I did 80m^2 * 60m^2=c^2. I ended up getting 100m=c. So since there were 4 of the little crisscrosses or hypotenuses I multiplied that by 4 to get 400m. I then added the 400m to the 160m from earlier to get 560m. Page 6 of 14 Student 28 Each player will run about 1.8 kilometers. Student 29 Each player has to run 1.68 kilometers. Bonus: The team at my school Student 30 Each player will run 560 meters per "double V." So each © 1994-2016 Drexel University http://mathforum.org/pows/ But since they ran it three times I multiplied that by three to get 1680m. But since they were asking for the distance in kilometers I divided that by 1000 to get 1.68km. First I took the 2 sides which were each 80 and I added them together to gat 160 meters. Then because I knew that they ran along the hypotenuse of a 45-45-90 triangle I used the formula a* the square root of 2. So I did 80(side length) * square root of 2 and found that the hypotenuse was about 113 meters long. Because the players run the triangle 4 times I multiplied 113 by 4. My answer was 452 meters. Then I added the 160 from before on to that. And then because the players run it 3 times I multiplied that by 3. I got a total of 1837 meters. To convert it into kilometers, I divided it by 1000. That is how I got 1.837 kilometers which I rounded to about 1.8 kilometers that each player runs each pratice during the Double V. First of all if we look closely at the field it is split into 4 right triangles. Because we know that the Pythagorean Theorem is a2+ b2= c2, and that it only works on right triangles we know that we can use the Pythagorean Theorem for this triangle. If we know that half of the length of the field is the bottom leg of the triangle we need to calculate it. So we divide 120 meters by 2 to get 60 meters for the base. Now we plug in 60 meters for a and 80 meters for b. We should come up with 3600 meter2 + 6400 meters2= c2. We add 3600 meters2 and 6400 meters2 together and get 10,000 meters2. Now we know that 10,000 meters2 is c2 we need to find the square root of it. The square root of 10,000 meter2 is 100 meters. So 100 meters is the hypotenuse or the diagonal run. Then we multiply it by 4 because there are 4 diagonal runs and we add the two 80 meter runs on the sides to get 560 meters per a double-V run. Since each player runs this 3 times, so we multiply 560 meters by 3 to get 1680 meters. To convert it to kilometers, we divide this by 1000 to get 1.68 kilometers. Bonus: To calculate rectangular field perimeter we have 75 yards + 75 yards + 115 yards + 115 yards and get 380 yards for one lap. Now we have to multiply it by 5 because there are 5 laps and get 1900 yards. (Note: 1yd = 0.9144m & 1m= 1.0936yd) To convert it to meters we multiply 1900 yards by 0.9144. We get about 1737m for the 5 laps. So the 5 laps have more of a distance. What: What I did was first I used the Pathagorean Thereom to clculate the hypotenuse per half feild. Half of a "V" is 100 meters long. This meant that every "double V" is 200 meters long. I then Page 7 of 14 student runs about 1680 meters which is 1.68 of a kilometer. added the rest of the sides together and got 560 meters for every "double V." I took that "double V" an mutiplied it by three because that is how many times each player runs the "double V." Lastly, I got 1680 meters and converted that to kilometers and got 1.68 kilometers. Why: I did it this way because I knew once I had the hypotenuse of half the diagnal it would be easy from there. The hypotenuse is 100 meters long and since it's a "V" I needed to double it. Then, I added the rest of the sides to that value. Each "double V" is about 560 meters long. lastly I mutiplied the "double V" by three because the players run it three times. Each player runs 1680 meters which is about 1.68 kilometers. Student 31 The players run 1.68 km in 3 double-v laps. Steps: 1. I found the length of the hypotenuse by using the pathagoreen thereom. Each side is 100 meters. 2. I doubled that to get the whole length of the "V." 200 meters. 3. I added the rest of the lengths of the sides to the "double V." 560 meters. 4. With the 560 meters per "double V" I mutiplied it by three which is how many times the player has to run it. That was 1680 meters long. 5. I then converted that to kilometers which is 1.68 kilometers. First I used tha pythagorean thereom of a^2 + b^2 = c^2> I substituted in a and b as 60 meters^2 + 80 meters^2 = c^2. After solving that I got 10,000 meters = c^2.C equals the square root of 10,000 so c = 100 meters. The v's equal 200 meters and the sides are 80 meters.When you add them up you get 1 lap as 560 meters. When you multiply that lap by 3 you get 1,680 meters as three laps. Since 1,000 meters equal 1 kilometer, I divided 1,680 meters by 1000 meters to get 1.68 kilometers as three laps Student 32 The soccer team should run 2.24 kilometers each day. © 1994-2016 Drexel University http://mathforum.org/pows/ To start out my POW, I calculated the hypotenuse of the squares, or halves of the court. To do this, I performed the operation of 80 meters squared + 60 meters squared (because half of the court length Page 8 of 14 Student 33 each player ran 800 meters. Student 34 The answer to the problem of the week is 1680 meters, or 1.68 kilometers. The answer to the extra credit is that the team that ran the Double Vs and they ran 1378.1 more meters. © 1994-2016 Drexel University http://mathforum.org/pows/ is 60) = c squared. 80^2+60^2 = C^2 I then multiplied each of these numbers out to further complete the problem. (80*80)= 6400 + 3600 = (60*60) = C^2 I then added these two numbers together so I could solve for C. 6400 + 3600 = 10,000 or c^2 To find out the square root of 10,000, I plugged the number into my calculator and solved. 10,000 square rooted = 100 meters To find the total distance of the double V pattern, I added together the four hypotenuses and two side lengths together. (100*4) + (80*2) = 400 + 160 or 560 meters. Because the team runs 3 of these patterns, I multiplied this by 3. 560 meters * 3 = 1,680 meters. The problem said that I should answer in kilometers, so I converted 1,680 meters into 1.68 kilometers. i first found out that it wasn't a square because it was 80by60 for each rectangle. then i realized where the lines intersected for each recatangle was the center. from number 5 to 4 was 160 meters because if the side length was 80 then because the recatangle divided by 2 is a right triangle and the hypotnuse is 2 * the smaller length. so 80 * 2 = 160. so then if the left side is congruent to the right side then it would be 6 to 5 is 80, 5 to 4 is 160 4 to 3 is 160 3 to 2 iis 80, 2 to 1 is 160 and 1 to 6 is 160 so the equation is 80 + 160 +160 + 80 + 160 +160 = 800. The way that I solved this problem is by first finding out the length of the diagnal. To find this, I used the pythagorean theorem which is a^2+b^2=c^2. I plugged in the numbers and got that c^2=10,000. I took the square root of that and got 100 meters. I took all of the lengths that were ran and got 560. It says that they ran the Double V three times, so I times the 560 by 3 to get 1680 meters. I divided that by 1,000 to get 1.68 kilometers. Extra Credit: I took the 75, I added a another 75, plus 2 115s to get the perimeter that they ran. I got 380. I times that by 5 because they ran 5 laps and got 1900. I then had to convert that into inches by timesing 1900 by 36 because there are 36 inches in a yard. I then had to convert that into meters by dividing that by 39 because there are 39 inches in a meter. I got 292.3. I subracted 292.3 meters from 1680, and got Page 9 of 14 Student 35 They have to run .56 kilometers. Student 36 Each soccer player runs about 1.68 kilometers during each practice session. Student 37 Each player runs 1.8376 kilometers. Student 38 Each player runs 1.2 kilometers. Student 39 Each person ran 400 meters. © 1994-2016 Drexel University http://mathforum.org/pows/ 1378.1 meters. I found all the sides of one of the triangles by using the pathagorian therumand i knew that all of the triangles are congruent. Why I did what I did is because the triangles were right triangles and I knew both legs of the triangle. First, I knew that 1/4 of the soccer field was a triangle, 60 on one leg, 80 on the other. To find out the hypotenuse, I had to use the formula a^2+b^2=c^2, so my problem looked like this:(60*60)+(80*80)=c*c. 60*60=3600 and 80*80=6400. Those two numbers added together equaled 10000. The square root of that was 100, which is the hypotenuse. There are 4 "hypotenuses" in the soccer field in which the players ran in, so I multiplied 100 by 4. That equaled 400. Next, I added to that 160, because the players also ran two other sides that were both 80 meters and got 560 meters. Since the soccer players ran 3 of the double "V" pattern, I multiplied 560 by 3 and got 1680 meters. The problem says to put your answer in kilometers, and since there are 1000 meters in one kilometer, I divided 1680 by 1000 and got my answer, 1.68 kilometers. I figured that if the two 80 lengths were the hypontenous of a right triangle, than if you divided it by the square root of two, you would get 56.56 m. on every other side since the whole thing was symetrical. so I had 8 sides with lengths of 56.56 m(or 56.56*8) and 2 sides with lenghts of 80 m (or 80 *2) so I did the problem (80*20) + (56.56*8)and I got 1837.6 meters. then, to convert it to kilometers, I divided it by 1000 and got 1.837 kilometers. First, I had to divide the 2 triangles. I knew that one side was 120 m. and the other sides were the same, so I set it up like x + x = 120. x= 60. Then I noticed 2 Vs, which has four sides. I did 60 * 4 = 240. Then I noticed two sides to turn, which is 80 m., I did 80 * 2 = 160. Then I did 160 + 240 = 400, because I knew that if I add this up together, I would have the total of one lap. But, I noticed that he asked for 3 laps, which I could do 3 * 400 = 1200 m. Then he asked for kilometers, so I moved the decimal point three times to the left, which I got 1.2 km. To find the answer to this POW I needed to find some lengths. First I used the foumula for a parrlelagram to find the area of the rectangle. To do this I multiplied 120meters by 80meters. Then I divided the area by two to find the smaller rectangle in it. Then i divided the quotient by four to find the area of the triangle. Then by dividing the width by half I. Then i divided each triangle by Page 10 of 14 Student 40 Each player runs 1.68 kilometers while running this Double V pattern 3 times. Student 41 A person runs 612.56 meters in the double v run. Student 42 They must run 5.6 KM © 1994-2016 Drexel University http://mathforum.org/pows/ making a line from the top to the bottom making a right angle. Then using the 30 60 90 formula i found the lengths i needed. Since the line are congruent i just muliplied the line by how many diangle lines. Then i added that to both of the sides with 80 meters to get my answer. the length of the field is 120 meters, and the width of the field was 80 meters. half of one V can be pictured as the hypotenuse of a right triangle. half of the field's length is 60 ( 120 / 2 ) and the width is the kept same. using the pythagorean theorum, a(a) + b(b) = c(c) you can find the lenth of the hypotenuse. 60(60) + 80 (80) = c(c) 3600 + 6400 = c(c) 10000 = c(c) = c(squared) (the square root of) 10000 = the square root of c(squared) 100 meters is c = c is 100 since there are two halves of the V to make a complete V, multiply the length of the hypotenuse of the right triangle by two. 100 x 2 = 200 meters since there are two V's to be run, multiply 200 by 2 = 400 meters since the runners must also run th width of the field twice, multiply the length of the width of the field by 2 ( 80 m x 2 = 160 meters ). then add the length of the two V's and the length of the width(2). 400 + 160 = 560 meters ran. there are 1,000 meters in a kilometer so 560 meters is equal to 0.56 kilometers. since each player runs this double V pattern 3 times, multiply 0.56 kilometers by 3. ==> 0.56 km x 3 = 1.68 kilometers To find the answere I needed to find the length of one v so i can double it and find the total of both the v's and i all ready know the rest lenghts.to find the length of v you divide it by half and now in one half of the rectangle you have a right angle.to find that length you need to take one of the smaller length and time it by The squre root of 2.and you get the ansewerand times by four and add 160 and get the answere. To solve this POW you can use many formulas, such as the tangent sine and cosine, but I chose the Pythagorean theorem. What I did was divided the rectangle into two squares, then I divided the two squares into two triangles so it looked like this…(the drawing stayed on word) Page 11 of 14 Student 43 Each player ran 1.68 kilometers. Student 44 Each player runs 1.68 kilometers. Student 45 1.680km © 1994-2016 Drexel University http://mathforum.org/pows/ In order to find the “red lines” [the hypotenuse] you can use the Pythagorean theorem the hypotenuse is 100m, since there are four hypotenuses I multiplied 100 by 4 to get 400m but there also 2 times when the players must run straight on “the legs” and that means you must add another 160 so the total is 560m, or 5.6 km…Each person must run 5.6 km. Bonus: Your team runs the perimeter (380 m) 5 times, the other runs the double V 3 times. You run a total of 1900 m and the other school runs a total of 1680 m. Your school runs more. First, I used the formula a^2 + b^2 = c^2 to find out that the diagonal of half the field is 100 meters. Then I added together all the measurements (100+10+100+100+80+80) to get 560. Then I multiplied that by three because the Double V was ran three times. I got 1,680. Then. because the answer had to be in kilometers and because a kilometer is 1,000 meters, I divided 1,680 by 1,000. My final answer was 1.68 kilometers. First, I found out what the length of half the field was, which came out to be 60. I did this so I could add it into the hypotenhuse formula. Next, I added the information into the hypotenhuse formula. I did this to find the hypotenhuse which came out to be 100. Siince there were 400 diagonal lines and 1 down line, I added 100+100+100+100+80+80. I did this to find the distance of one lap which was 560 merters. I multiplied that by three. I did this because each player has to run around the course three times. After coming up with 16080 meters I converted it to kilometers and got 1.68 kilometers. This question has to ways of finding the answer. The first way is the most noticeable one. This way you look at a corner and you will see a big triangle. (I used the triangle 423.) When you see this triangle you notice that it has a right angle, this means you could use the Pythagorean Theorem to find out one edge of it (or in other words half of one V.) To use the formula you need to know 2 of the sides, and you already know one and that is the 80 meters. The other side that you use is the perimeter of the rectangle; to find this one you divide 120 by 2 because it goes to the center line. This gives you 60. Now because we are using the Pythagorean Theorem we need to square 80 and 60 and then add them up which you would get 10000. Because this equals C sq you need to find the square root of it which is 100. So 100 is half of a V and because there is 2 V’s you multiply 100 by 4 to get 400. Now because they also run the 80m Page 12 of 14 Student 46 Each player runs 1.68 kilometers if they do the "double V" 3 times.My explanation is as follows. on both sides you need to multiply 80 by 2 and then add it to 400 and then you would get 560. Then because they run the lap 3 times you multiply that by 3 to get 1680m so to get one kilometer (1000 meters) you would divide by 1000 to get 1.680km. Another way to do this (which isn’t that obvious) is to look at any of triangles on the edges right or left side (I used the one on the right edge), at first you see that I doesn’t have a right angle, but if you cut it in half and then you would have a right angle. Now because one of it’s corners start midway between 80 meters you use 40 and because when you divided it in half you made a line that goes ¼ the way across the field so 120/4=30, so you have 30sq and 40sq because of the Pythagorean Theorem which adds up to 2500. Now because that equals C sq and I want C, so I need to find the sq root of C sq which is 50 so the other edge of that triangle is 59. Now because there are 8 of those little lines you do 50 times 8 which equals 400, then because you run an extra 80 meters twice you add 160 to it getting 560. Then because they ran 3 laps it is multiplied by 3 which is 1680, then because it is in kilometers you divide by 1000 getting 1.680. I knew the length of the soccer field is 120 meters and the width of the soccer field is 80 meters, so to find the length of the diagonal line I had to cut the 120 in half because the end of the diagonal line is at the center. So my 2 dimensions are 60 and 80 for the shape of the right triangle on one of the sides of the diagonal line. If you add the square of the first leg of the right triangle which, in this case is 60 meters, and the square number of the second leg you would come up with the area of the square off the hypotenuse, which ,in this case, equals 10,000.So I had to find the square root of 10,000, and that would give me the length of the hypotenuse. I knew that the square root of 10,000 would have to be more than 80 because that is the length of the longest leg and the hypotenuse is longer than both of the legs, so I tried 100. So I did 100 times 100 and got 10,000 so the length of the hypotenuse is 100 meters. So if one of the diagonal lines is 100 meters and all of the diagonal lines are equal, then that means all of the other diagonal lines are 100 meters long. So I added up all 4 diagonal lines and got 400. But I still have to add the two 80s to the 400, so I added them and got 560 meters. Then it said that the players had to run the double V three times so I multiplied 560 by three and I got 1680 meters. But I still have to find the number of the kilometers that the players ran, and I knew that there are 1,000 meters in one kilometer, so I have one full kilometer. But I still have the left over 680 meters so I know that if I had 500 meters left I would have .5 kilometers, so for this I have .68 kilometers and so the full amount of kilometers that the players ran is 1.68. Student 47 Student 48 Each player ran 1.68 kilometers. © 1994-2016 Drexel University http://mathforum.org/pows/ I looked part of this problem up on the internet. I looked on google and found a formula:a squared+b squared =c squared. The hypotenuse(the long side) is c squared, which is what I was trying to find. I already knew that a equaled 80 meters, and b equaled 60 meters. That means I'm doing (80x80)+(60x60). 80x80=6,400, and 60x60=3,600. Now I'm Page 13 of 14 Student 49 My answer is 1.68 kilometer. doing 6,400+3,600, which equals 10,000. This number is c squared. I had to find the square root of 10,000, which is 100. Now I have the plain line of c. This soccer field has 2 sides that equal 80 meters, so I know that each player runs at least that much. They all run the "Double V" 3 times, so that means I'm now doing 160x3. That gave me 480. Next, in each lap around the "Double V", they run the 100 meter stretch 4 times, so I know that they each run at least 400 meters. Again, they each run the "Double V" 3 times, so I now need to do 400x3. Now I have 1,200. Finally, I need to add 480 and 1,200. That got me to 1,680. As my final few steps, I can take off the zero and put in a decimal point. My sure answer is 1.68 kilometers run by each player. I got my anwer by doing algebra. First I had to find the length of each leg of a right triangle. The length of the verticle leg is 80 meters because the triangle length is the same as the height of the rectangle which is 80 meters. Next I had to find the horizontal leg which is 60 meters because the whole length of the rectangle is 120 meters and the leg is half of the 120 meters which is 60 meters.The rule is A squared + B squared = C squared. A is 80 meters so you have to square it 80x80=6,400. Next you have to do B squared which is 60x60=3,600. So now you have to add 6,400+3,600=10,000 , next I have to find the square root of 10,000 because C squared is the same as C(C), and I need to know what one C equals. 100x100=10,000, C=100. So I figured out the length of C, which is the length of all the diagonals. The length of the circuit is 560 meters. So if they have to do three laps that equals 560x3=1,680 meters. If there are 1,680 thats one kilometer and 680 is basically is .68 so the answer is 1.68 kilometers. Student 50 © 1994-2009 Drexel University http://mathforum.org/pows/ © 1994-2016 Drexel University http://mathforum.org/pows/ Page 14 of 14