In a right triangle, the length of the longer leg is 7 more inches than the shorter leg. The length of the hypotenuse is 8 more inches than the length of the shorter leg.

Question

A). If the shorter leg is representd by x, write expressions for the longer leg and the hypotenuse in terms of x

B). Write an equation using the Pythagoreum Theorem that relates the three sides together and solve it for the value of x. Then identify the lengths of the longer side and hypotenuse.

Answer 1

B.
(x+7)^2 + x^2 = (x+8)^2

x^2 + 14 x + 49 + x^2 = x^2 + 16 x + 64

x^2 - 2 x - 15 = 0

(x-5)(x+3) = 0
so
x = 5
x + 7 = 12
x+8 = 13