Chapter 8.2, Problem 13WE

To determine

To find: the length of the diagonal

Answer to Problem 13WE

  $AC=3$

Explanation of Solution

Given:

The rectangle has length 2.4 and width 1.8.

Draw a rectangle of length 2.4 and width 1.8 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 7 and 24.

So, by Pythagoras theorem,

  $\begin{array}{c}A{C}^2=A{D}^2+D{C}^2\\ x^2={1.8}^2+{2.4}^2\\ x^2=3.24+5.76\\ x^2=9\end{array}$

Now, take square root of both sides,

  $\begin{array}{c}\sqrt{x^2}=\sqrt{9}\\ x=3\end{array}$