# A square has a diagonal with the length of 6 meters, how do you find the lengths of the sides of the square?

Aug 1, 2017

$3 \sqrt{2}$

#### Explanation:

$\text{the diagonal splits the square into 2 congruent right angled}$
$\text{triangles}$

$\text{choosing 1 right triangle and applying "color(blue)"Pythagoras' theorem}$

$\text{let the side of the square } = x$

$\text{the diagonal is the hypotenuse of the triangle}$

$\Rightarrow {x}^{2} + {x}^{2} = {6}^{2} \leftarrow \textcolor{b l u e}{\text{ Pythagoras' theorem}}$

$\Rightarrow 2 {x}^{2} = 36$

$\text{divide both sides by 2}$

$\Rightarrow {x}^{2} = 18$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\Rightarrow x = \pm \sqrt{18} \leftarrow \text{ length must be positive}$

$\Rightarrow x = \sqrt{18} = \sqrt{9} \times \sqrt{2} = 3 \sqrt{2}$