# How do you determine if the lengths 36, 77, 85 form a right triangle?

Jan 16, 2017

Use the Pythagorean theorem. See the entire determination process below:

#### Explanation:

We will use the Pythagorean Theorem to determine if these lengths for a right triangle.

This theorem states, for a right triangle:

${a}^{2} + {b}^{2} = {c}^{2}$

Where $a$ and $b$ are the base and height and $c$ is the hypotenuse which is also the longest length.

Substitute the values into this equation and see if both sides of the equation are equal. If they are the lengths form a right triangle. If they are not equal then they would not form a right triangle.

${36}^{2} + {77}^{2} = {85}^{2}$

$1296 + 5929 = 7225$

$7225 = 7225$

Because both sides of the equation are equal these lengths do form a right triangle.