# What is the perimeter of a square whose diagonal is 3sqrt2?

Apr 28, 2016

The perimeter would be 12 units.

#### Explanation:

To find the perimeter of a square with a diagonal of $3 \sqrt{2}$ we must first determine the length of the sides of the square.

A square cut by a diagonal is divided into a ${45}^{o} - {45}^{o} - {90}^{o}$ triangle which has a special ration of $a - a - a \sqrt{2}$

This means the sides of the square are $s = 3$

The perimeter of a square is determines by the equation $P = 4 s$

$P = 4 \left(3\right) = 12$