The length of the longer length is 32 cm.
Work Step by Step
Let $x$ cm be the longer length. Since the hypotenuse is 8 centimeters longer than the longer leg, the hypotenuse = $x + 8$. And, the shorter leg is 8 centimeters shorter than the longer leg, the shorter leg = $x - 8$ By Pythagoras Theorem, $x^2$ + $(x - 8)^2$ = $(x + 8)^2$ $x^2 + x^2 - 16x + 64 - x^2 - 16x - 64 = 0$ $x^2 -32x = 0$ $x(x - 32) = 0$ $x = 0$ (rejected) or $x = 32$ Hence, the length of the longer length is 32 cm.