How long should the sides of the triangle​ be?

Question

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?

Answer 1

Let x be the length of the shorter leg, y the longer leg and h the hypotenuse

h²= x² + y²

(x+12)² = x² + (x+6)²

x²+24x+144 = x² + x² + 12x + 36

x²-12x -108 = 0

(x-18)(x+6) = 0 x = 18,-6 take the positive number

y = x+6 = 24

h = x+12 = 30

The sides are 18,24,30

Answer 2

H=12+S

L=6+S

H^2 = S^2 + L^2

(12+S)^2 = S^2 + (6+S)^2

144 + 24S + S^2 = S^2 + 36 + 12S + S^2

S^2 -12S - 108 = 0

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

S= 6 or 18

L = 12 or 24

H= 18 or 30

18^2 + 24^2 = 324 + 576 = 900 = 30^2

Answer is S=18, L=24, H= 30

6^2 + 12^2 = 36+ 144 = 180 but 18^2 = 324

only answer is 18, 24 and 30 cm

It's a 3-4-5 right triangle with each side multiplied by a factor of 6