Chapter 8.2, Problem 16WE

To determine

To find: the length of side of square.

Answer to Problem 16WE

  $6\sqrt{2}$

Explanation of Solution

Given:

The square has a diagonal of length 12.

Draw a square with diagonal of length 12 and label it as $ABCD$ .

And let the side of the square be x.

Consider the right triangle $△ADC$ .

Now, $\overline{AC}$ is the hypotenuse and has length 12 and the lengths of the legs is x.

So, by Pythagoras theorem,

  $\begin{array}{c}A{C}^2=A{D}^2+D{C}^2\\ {12}^2=x^2+x^2\\ 144=2x^2\end{array}$

  $\begin{array}{c}\frac{144}{2}=\frac{2x^2}{2}\\ 72=x^2\end{array}$

Now, take square root of both sides,

  $\begin{array}{c}\sqrt{x^2}=\sqrt{72}\\ x=6\sqrt{2}\end{array}$

The length of side of square is $6\sqrt{2}$ .