Question

Determine the exact length of the diagonal of a,square if the perimeter of the square is 24

ft. Give the answer in simplest radical form.
Perimeter = 24
d=

Answer 1

`6\sqrt2`

Explanation:

First, we need to find the length of one side. Since it's a square and we have our perimeter of 24, we simply divide that by 4 to get a side length of 6.
When you split a square diagonally, it forms two special 45-45-90 triangles. With such triangles, the leg lengths are x and x, and the hypotenuse is
`x\sqrt2`. Therefore, your answer is
`6\sqrt2`.

I've enclosed a picture to help.