I need help solving this equation

Question

The longer leg of a right triangle is 1 meter longer than the shorter leg. The hypotenuse is 1 meter shorter than twice the short leg. Find the lengths of the sides of the triangle.

Answer 1

H=2S-1

L=1+S

H^2 = S^2 +L^2

(2S-1)^2 = S^2 + (1+S)^2

4S^2 -4S + 1 = S^2 + 1 + 2S + S^2

2S^2 -6S = 0

2S(S-3) = 0

S=3 meters= shortest side

L = 3+1 = 4 meters = longer side

H=2(3)-1 = 5 meters = hypotenuse

3^2 + 4^2 = 5^2

9 + 16 = 25