A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 6 cm more than the shorter leg and the hypotenuse 12 cm more than the shorter leg. How long should the sides of the triangle be?

18cm, 24cm, 30cm

Step-by-step explanation:

Let x be the length of the shorter leg

(x + 12) ² = (x + 6) ² + x²

x² + 24x + 144 = x² + 12x + 36 + x²

x² - 12x - 108 = 0

x² - 18x + 6x - 108 = 0

x (x - 18) + 6 (x - 18) = 0

(x - 18) (x + 6) = 0

x = 18, - 6

x = 18

x + 6 = 24

x + 12 = 30