# How do you use the Pythagorean Theorem to determine if the following three numbers could represent the measures of the sides of a right triangle: 9 in, 12 in, 15 in?

Mar 20, 2016

They DO represent the measures of the sides of a right triangle.

#### Explanation:

The Pythagorean Theorem states that:
${a}^{2} + {b}^{2} = {c}^{2}$, with $a$ and $b$ being the legs of a right triangle, and $c$ being the hypotenuse. We can substitute 9, 12, and 15 into the formula to see if it works.

The hypotenuse will always be the longest side of the right triangle, so in this case, 15 is the hypotenuse.
${9}^{2} + {12}^{2} = {15}^{2}$
$81 + 144 = 225$
$225 = 225$

Therefore, 9 in, 12 in, and 15 in are the measure of the sides of a right triangle.