###### Example10.9.1

You may be familiar with the Pythagorean Theorem: If the legs of a right triangle have lengths of \(a\) and \(b\) while the hypotenuse has a length of \(c\text{,}\) then

Suppose that we have a right triangle where one leg is \(1\) inch longer than the other leg and the hypotenuse is \(1\) inch longer than the longer leg. Determine the length of each side of the triangle.

Let \(x\) represent the length (in) of the shorter leg of the triangle. Then the length (in) of the longer leg is represented by \(x+1\) and the length (in) of the hypotenuse is represented by \(x+2\text{.}\)

Applying the Pythagorean Theorem we have

We begin solving the equation by expanding all expressions in the equation.

Since a length cannot be negative, we reject the negative solution. So the lengths of the triangle are \(3\) inches, \(4\) inches, and \(5\) inches.