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The shorter leg of a right triangle is 9 ft shorter than the longer leg. The hypotenuse is 9 ft longer than the long leg. Find the sides of the triangle

 Feb 8, 2021
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Let L ft be the length of the shorter leg.

 

Length of longer leg = L + 9

 

Length of hypotenuse = (L + 9) + 9 = L + 18

 

By Pythagorean theorem,

L^2 + (L + 9)^2 = (L + 18)^2

2L^2 + 18L + 81 = L^2 + 36L + 324

L^2 - 18L - 243 = 0

(L - 27)(L + 9) = 0

L = 27 or L = -9 (rejected)

 

Therefore the shorter leg is 27 ft, longer leg is (27 + 9) ft = 36 ft, hypotenuse = (27 + 18) ft = 45 ft.

 Feb 8, 2021

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