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

Let the shorter leg = a.

The longer leg, b = a + 4.

The hypotenuse, c = a + 8

a^2 + b^2 = c^2

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

a^2 + a^2 + 8a + 16 = a^2 + 16a + 64

a^2 - 8a - 48 = 0

(a - 12) (a + 4) = 0

a - 12 = 0 or a + 4 = 0

a = 12 or a = - 4

a = - 4 is discarded because it is negative.

a = 12

b = 16

c = 20

The lengths are 12 m, 16 m, and 20 m.