# How do you find the length of the hypotenuse of a triangle with sides of length √5m and 3√2m?

Jun 10, 2016

$\sqrt{23}$

#### Explanation:

A right-angled triangle with legs of lengths $a$ and $b$, and a hypotenuse of $c$ has the lengths of its sides specified by the Pythagorean Theorem:
$\textcolor{w h i t e}{\text{XXX}} {c}^{2} = {a}^{2} + {b}^{2}$

For the given case $a = \sqrt{5} m$ and $b = 3 \sqrt{2} m$

Therefore
$\textcolor{w h i t e}{\text{XXX}} {c}^{2} = {\left(\sqrt{5}\right)}^{2} + {\left(3 \sqrt{2}\right)}^{2}$

$\textcolor{w h i t e}{\text{XXXX}} = 5 + 18$

$\textcolor{w h i t e}{\text{XXXX}} = 23$

So
$\textcolor{w h i t e}{\text{XXX}} c = \sqrt{23}$