# How do you find the perimeter of a square with a diagonal of 12 cm?

Oct 17, 2015

$24 \sqrt{2}$

#### Explanation:

diagonal of the square is $s \sqrt{2}$

$s \sqrt{2}$ = $12$

$s$ = $\frac{12}{\sqrt{2}}$

$s$ = $\frac{12}{\sqrt{2}}$ x $\frac{\sqrt{2}}{\sqrt{2}}$

= $12 \frac{\sqrt{2}}{\sqrt{4}}$

= $12 \frac{\sqrt{2}}{2}$

= $6 \sqrt{2}$

perimeter of the square is $4 s$

$4 \left(6 \sqrt{2}\right)$ = $24 \sqrt{2}$