It’s a algebra question

Question

One leg of a right triangle is 7 inches more than twice the length of the other leg. The hypotenuse is 8 inches more than the shorter leg. find the lengths of all the sides.

Answer 1

L=7+2S

H=8+S

H^2 = L^2 + S^2

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

64 + 16S + S^2 = 49 +28S + 4S^2 + S^2

4S^2 +12S -15 = 0

S^2 + 3S = 15/4 complete the square, take half of 3 and square it, (3/2)^2 = 9/4, add to both sides

S^2 + 3S + 9/4 = 15/4 + 9/4

(S +3/2)^2 = 24/4 = 6

S +3/2 = + or -sqr6

S = -3/2 + sqr6 = about 2.45- 1.5 = 0.95 inches

L = 7+2(.95) = 8.9 inches

H = 8+.95 = 8.95 inches

8.95^2 = about 8.9^2 + 0.95^2

80.1 = about 79.21 + .90= 80.1