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.