SOLUTION: One leg of right triangle is 9 inches shorter than the other leg. The hypotenuse is 45 inches. What is the length of all sides?
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Question 534861: One leg of right triangle is 9 inches shorter than the other leg. The hypotenuse is 45 inches. What is the length of all sides? Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! One leg of right triangle is 9 inches shorter than the other leg. The hypotenuse is 45 inches. What is the length of all sides?
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Let x = length of "other leg"
then
x-9 = 2nd leg
.
applying Pythagorean theorem:
x^2 + (x-9)^2 = 45^2
x^2 + (x-9)(x-9) = 45^2
x^2 + x^2-18x+81 = 2025
2x^2-18x+81 = 2025
2x^2-18x-1944 = 0
x^2-9x-972 = 0
(X+27)(x-36) = 0
x = {-27, 36}
throw out the negative answer leaving:
x = 36 inches
.
Answer: the three sides are:
36, 27, and 45 inches
