A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 8 cm more than the shorter leg and the hypotenuse 16 cm more than the shorter leg. how long should the sides of the triangle be?

Let x be the length of the shorter side. legs are x and x+8, hypotenuse it's x+16

x² + (x+8) ² = (x+16) ²

x²+x²+16x+64=x²+32x+256

2x²+16x+64=x²+32x+256

x²-16x-192=0

(x-24) (x+8) = 0

x = 24 or - 8. since length cannot be negative, 24 is the short side, 32 is the long side, and 40 is the hypotenuse