Question 31210
First find the length of one side (s) of the square.

The perimeter of a square is 4s and this = 32
So, s = 32/4 = 8

Now you can use the pythagorean theorem to find the length of the diagonal (d).

The diagonal (d) is the hypotenuse of the right triangle whose other two sides are s and s.

{{{d^2 = s^2 + s^2}}}
{{{d^2 = 2s^2}}} But s = 8, so:
{{{d^2 = 2(8)^2}}} Take the square root of both sides of the equation.
{{{d = sqrt(2)(8)}}}

The length of the diagonal is:
{{{d = 8sqrt(2)}}}