Chapter 8.2, Problem 9WE

To determine

To find: x

Answer to Problem 9WE

  $x=25$

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, $BC=7$ and $CD=24$

Consider the right triangle $△ADC$ .

Now, $\overline{AC}$ is the hypotenuse and has length x and the lengths of the legs are 7 and 24.

So, by Pythagoras theorem,

  $\begin{array}{c}A{C}^2=A{D}^2+D{C}^2\\ x^2=7^2+{24}^2\\ x^2=49+576\\ x^2=625\end{array}$

Now, take square root of both sides,

  $\begin{array}{c}\sqrt{x^2}=\sqrt{625}\\ x=25\end{array}$