SOLUTION: One leg of a right triangle is 7in longer than the smaller leg, and the hypotenuse is 8in longer than the smaller leg. Find the lengths of the sides of the triangle.

Question 400983: One leg of a right triangle is 7in longer than the smaller leg, and the hypotenuse is 8in longer than the smaller leg. Find the lengths of the sides of the triangle.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the smaller leg
Let = longer leg
Let = hypotenuse
given:
in
in
It's a right tringle, so

By substitution:

I can complete the square to find

Both sides are now a perfect square

Take the square root of both sides

It is also true that
, but I can't use a negative result
Since

and, since

The sides are 5, 12, and 13
check answer:

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