Pythagorean theorem

Question

The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. The length of the hypotenuse is 22 inches more than twice the length of the shorter leg. Find the side lengths of the triangle.

Answer 1

L=20+2S

2S=L-20

S = L/2 -10

H=22+2S

H=2+L

H^2 = L^2 + S^2

(2+L)^2 = L^2 + (L/2 - 10)^2

L^2 + 4L + 4 = L^2 + L^2/4 -10L + 100

L^2/4 -14L +96=0

L^2 - 56L + 384 =0

L^2 -56 + 28^2 = -384 + 28^2

(L-28)^2 = 1168

L-28 = 34.2

L = 28+34.2 = 62.2 inches

S=L/2-10 = 21.1 inches

H = 64.2 inches