Chapter 8.2, Problem 14WE

To determine

To find: the width of the rectangle.

Answer to Problem 14WE

  $1$

Explanation of Solution

Given:

The rectangle has a diagonal of 2 and length of $\sqrt{3}$ .

Draw a rectangle with diagonal of 2 and length of $\sqrt{3}$ and label it as $ABCD$ .

And let the width of the rectangle be x.

Consider the right triangle $△ADC$ .

Now, $\overline{AC}$ is the hypotenuse and has length 2 and the lengths of the legs are $AD=x$ and $DC=\sqrt{3}$ .

So, by Pythagoras theorem,

  $\begin{array}{c}A{C}^2=A{D}^2+D{C}^2\\ 2^2=x^2+{\left(\sqrt{3}\right)}^2\\ 4=x^2+3\end{array}$

  $\begin{array}{c}{x}^2=4-3\\ x^2=1\end{array}$

Now, take square root of both sides,

  $\begin{array}{c}\sqrt{x^2}=\sqrt{1}\\ x=1\end{array}$