The shorter leg of a right triangle is 6m shorter than the longer leg. the hypotenuse is 6m longer than the longer leg. find the side lengths of the triangle.

Short leg = x-6m

Longer leg = x

Hypotenuse = x+6m

x² + (x-6) ² = (x+6) ²

x² + x²-12x+36 = x²+12x+36

2x²-12x+36 = x² + 12x+36

2x²-12x+36-36 = x² + 12x+36-36

2x² - 12x-12x = x²+12x-12x

2x² - 24x-x² = x²-x²

x² - 24x = 0

x (x-24) = 0

x = 24

Short leg = 24-6m = 18

Longer leg = 24

Hypotenuse = 24+6m=30

Check

a² + b² = c²

18² + 24² = 30²

324 + 576 = 900

900=900