The longer leg of a right triangle is 4cm longer than the shorter leg the hypotenuse is 8 cm longer than the shorter find the side lengths of the triangle

Let x be length of shorter leg

4cm longer than the shorter leg x + 4 = length of longer leg

hypotenuse is 8 cm longer than the shorter

x + 8 = length of hypotenuse

phytagorus rule

x^2 + (x+4) ^2 = (x+8) ^2

x^2 + x^2 + 8 x + 4^2 = x^2 + 16x + 8^2

x^2 - 8x - 48 = 0

(x + 4) (x - 12) - 0

x = - 4 we reject negative number

so x = 12