SOLUTION: A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is the distance?

Algebra ->  Pythagorean-theorem -> SOLUTION: A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is the distance?      Log On


   

Question 597354: A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is the distance?
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is the distance?
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Hi, there--
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To solve this problem, notice that the diagonal divides the rectangle into 2 congruent right triangles (same size, same shape).
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The two legs of each right triangle are 90m and 120m. The diagonal is the hypotenuse of each right triangle. (Draw a diagram of the soccer field with these measurements.)
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We'll use the Pythagorean Equation to find the length of diagonal. Let's call the length of the legs of the triangle a and b. We'll call the length of the diagonal c.
a%5E2%2Bb%5E2=c%5E2
%2890%29%5E2%2B%28120%29%5E2=c%5E2
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Simplify.
8100%2B14400=c%5E2
22500=c%5E2
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To find the value of c-squared, take the square root of both sides of the equation. c is 150 since 150*150=22500.
c=150
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The length of the diagonal is 150 meters.
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That's it! Feel free to email me via gmail if the explanation is unclear.
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Ms.Figgy
math.in.the.vortex@gmail.com