The shorter leg of a right triangle is 8 centimeters less than the other leg. Find the length of the two legs if the hypotenuse is 40.

Long leg = x

short leg = x - 8

hypo = 40

x^2 + (x-8) ^2 = 40^2

x^2 + x^2 - 16x + 64 = 1600

2x^2 - 16x - 1536 = 0

2 (x^2 - 8x - 768) = 0

(x - 32) (x + 24) = 0

x - 32 = 0; x = 32

x + 24 = 0; x = - 24

so

long leg = 32

short leg = 32 - 8 = 24