SOLUTION: Quadratic Equations The hypotenuse of a right triangle measures 20cm. The sum of the lengths of the legs is 28cm. Find the length of each leg of the triangle.

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Question 177827: Quadratic Equations
The hypotenuse of a right triangle measures 20cm. The sum of the lengths of the legs is 28cm. Find the length of each leg of the triangle.
Answer by ankor@dixie-net.com(22740) (Show Source):
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The hypotenuse of a right triangle measures 20cm. The sum of the lengths of the legs is 28cm. Find the length of each leg of the triangle.
:
let x = one leg of the triangle
then
(28-x) = other leg
;
Pythagorus states
x^2 + (28-x)^2 = 20^2
;
x^2 + (784 - 56x + x^2) = 400
:
x^2 + x^2 - 56x + 784 - 400 = 0
:
2x^2 - 56x + 384 = 0
simplify, divide by 2
x^2 - 28x + 192 = 0
Factor
(x - 16)(x - 12) = 0
two solutions
x = 16, then the other leg = 12
x = 12, then the other leg = 16