# How do you determine if the lengths sqrt5, 7, 14 form a right triangle?

Mar 21, 2018

Plug them into the Pythagorean theorem
No, the side lengths do not form a right triangle.

#### Explanation:

The Pythagorean theorem: ${a}^{2} + {b}^{2} = {c}^{2}$, where $a$ and $b$ represent the two shortest sides (the legs of a right triangle) and $c$ is the hypotenuse (longest side of the right triangle opposite the right angle).

14 is the largest side.

Does ${\sqrt{5}}^{2} + {7}^{2}$ equal ${14}^{2}$?

$5 + 49$

$54$

${14}^{2} = 196$

$54 \ne 196$

$54 \ne {14}^{2}$