# How do you determine if the lengths 4, sqrt26, 12 form a right triangle?

Mar 8, 2017

See the entire solution process below:

#### Explanation:

We can use the Pythagorean Theorem to determine if these lengths form a right triangle.

The Pythagorean Theorem states, for a right triangle:

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

$a$ and $b$ are legs of the right triangle
$c$ is the hypotenuse of the right triangle

Substituting $4$ and $\sqrt{26}$ for $a$ and $b$ and substituting $12$ for $c$ gives:

${4}^{2} + {\left(\sqrt{26}\right)}^{2} = {12}^{2}$

$16 + 26 = 144$

$42 \ne 144$

These lengths for the sides of a triangle DO NOT form a right triangle.