The longer leg of a right triangle is 7 inches longer than the shorter leg. The hypotenuse is 9 inches longer than the shorter leg. Find the side lengths of the triangle.

Question

The longer leg of a right triangle is 7 inches longer than the shorter leg. The hypotenuse is 9 inches longer than the shorter leg. Find the side lengths of the triangle.

Answer 1

L=S+7

H=S+9

H^2 = L^2 + S^2

(S+9)^2 = (S+7)^2 + S^2

S^2 + 18S +81 = S^2 + 14S + 49 +S^2

S^2 -4S -32 = 0

(S-8)(S+4)=0

S = 8 inches = shorter side

L = 15 inches = longer side

H = 17 inches = hypotenuse

8^2 + 15^ = 64 + 225 = 289 = 17^2