Chapter 8.2, Problem 10WE

To determine

To find: x

Answer to Problem 10WE

  $x=9$

Explanation of Solution

Given:

The diagram:

Consider the figure shown below:

It can be observed that the given figure is a rectangle.

It is known that the opposite sides of a rectangle are equal. So, $DC=12$

Consider the right triangle $△ADC$ .

Now, $\overline{AC}$ is the hypotenuse and has length 15 and the lengths of the legs are $AD=x$ and $DC=12$ .

So, by Pythagoras theorem,

  $\begin{array}{c}A{C}^2=A{D}^2+D{C}^2\\ {15}^2=x^2+{12}^2\\ 225=x^2+144\end{array}$

  $\begin{array}{c}{x}^2=225-144\\ x^2=81\end{array}$

Now, take square root of both sides,

  $\begin{array}{c}\sqrt{x^2}=\sqrt{81}\\ x=9\end{array}$