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

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