The longer leg of a right triangle is 1inch longer than the shorter leg. the hypotenuse is 9inches longer than the shorter leg. find the side lengths of the triangle.

For right triangles, where a = shorter leg, b = longer leg, and c = hypotenuse:

This is the Pythagorean Theorem.
So they tell us that b is 1in longer than a:
b = a + 1
and hypotenuse (c) is 9in longer than a:
c = a + 9
Now we plug in the Pythagorean Theorem to solve for a:

From here, since not favorable with normal methods, use the quadratic equation to find a:

where b = -16, and c = -80


We can only have positive lengths in real-life, so our a = 20
Remember our original a was the shorter leg,
then b = a + 1 = 20 + 1 = 21 (our longer leg),
and our hypotenuse (c) = a + 9
c = 20 + 9 = 29
Now our triangle's sides are:
20 in, 21 in, and 29 in