Chapter 8.4, Problem 18WE

To determine

The perimeter of square

Answer to Problem 18WE

The perimeter of square is $16\sqrt{2}$

Explanation of Solution

Given information:

The diagonal of Square is 8.

Let the side of square be x then

  $\begin{array}{l}{h}^2=p^2+b^2\\ 8^2=x^2+x^2\\ 8^2=2x^2\\ 64=2x^2\\ x^2=32\\ x=4\sqrt{2}\end{array}$

Perimeter of square

  $\begin{array}{c}=4\times side\\ =4\times 4\sqrt{2}\\ =16\sqrt{2}\end{array}$

Therefore the perimeter of square is

  $16\sqrt{2}$