# The given lengths are: 24, 30, 6 square root of 41, do they represent the sides of a right triangle?

Oct 6, 2015

Yes.

#### Explanation:

To find out if these are the sides of a right triangle, we will check if the square root of the sum of the squares of the two shorter sides is equal to the longest side. We're going to make use of the Pythagorean theorem:

$c = \sqrt{{a}^{2} + {b}^{2}}$; where $c$ is the longest side (hypotenuse)

Okay, let's start by checking which are the two shorter lengths. These are 24 and 30 (because $6 \sqrt{41}$ is around 38.5). We'll substitute 24 and 30 into $a$ and $b$.

$c = \sqrt{{a}^{2} + {b}^{2}}$
$c = \sqrt{{24}^{2} + {30}^{2}}$
$c = \sqrt{576 + 900}$
$c = \sqrt{1476}$
$c = \sqrt{{6}^{2} \cdot 41}$
$\textcolor{red}{c = 6 \sqrt{41}}$

Since $c = 6 \sqrt{41}$, then the three lengths represent the sides of a right triangle.