I think this is how you do it, somebody correct me if I'm wrong.
one leg of a right triangle is 7 feet shorter then then other leg. => x-7
the hypotenuse is 2 feet longer then the longer leg => x+2
So the two sides are x, x-7, and the hypotenuse is x+2
By Pathagores theorum we know that (a^2)+(b^2)=(c^2)
So we have:
(x^2)+(x-7)^2 = (x+2)^2
we then get:
x^2 + x^2 -14x +49 = x^2 +4x +4
x^2 -18x +45 = 0
We factor to get:
(x-3)(x-15) = 0
So x can equal 3 or 15
Since one side is 7 less than x and we cant have negative length 3 cannot be an answer. So one side is 15, the other is 8, and the hypotonus is 17.