Chapter 8.2, Problem 15WE

To determine

To find: the length of the diagonal of the square.

Answer to Problem 15WE

  $4\sqrt{2}$

Explanation of Solution

Given:

The perimeter of square is 16.

Concept Used:

  $\text{Perimeter of square}=4\times \text{side}$

It is given that perimeter of square is 16.

Then,

  $\begin{array}{c}\text{Perimeter of square}=4\times \text{side}\\ 16=4\times \text{side}\\ \frac{16}{4}=\text{side}\\ 4=\text{side}\end{array}$

Draw a square of side 4 and label it as $ABCD$ .

And let the length of the diagonal $\overline{AC}$ be x.

Consider the right triangle $△ADC$ .

Now, $\overline{AC}$ is the hypotenuse and has length x and the lengths of the legs are 4 and 4.

So, by Pythagoras theorem,

  $\begin{array}{c}A{C}^2=A{D}^2+D{C}^2\\ x^2=4^2+4^2\\ x^2=16+16\\ x^2=32\end{array}$

Now, take square root of both sides,

  $\begin{array}{c}\sqrt{x^2}=\sqrt{32}\\ x=4\sqrt{2}\end{array}$