One leg of a right triangle is 3 millimeters longer than the shorter leg and the hypotenuse is 6 millimeters longer than the shorter leg. find the lengths of the sides of the triangle.

Suppose the shorter leg is x, then the longer leg is x+3, and the hypotenuse is x+6

x^2 + (x+3) ^2 = (x+6) ^2

x^2 + x^2 + 6x + 9=x^2 + 12x + 36

x^2-6x-27=0

(x+3) (3-9) = 0

x=-3, which is impossible, or x=9

so the shorter leg is 9mm, the longer leg is 12mm, and the hypotenuse is 15mm