Chapter 8.2, Problem 11WE

To determine

To find: x

Answer to Problem 11WE

  $x=8\sqrt{2}$

Explanation of Solution

Given:

The diagram:

Consider the figure shown below:

It can be observed that the given figure is a square as all the four angles of the quadrilateral are right angles and thus congruent and also the adjacent sides are congruent.

It is known that the all sides of a square are equal. So, $AD=8$ and $DC=8$

Consider the right triangle $△BAD$ .

Now, $\overline{BD}$ is the hypotenuse and has length x and the lengths of the legs are $AD=8$ and $AB=8$ .

So, by Pythagoras theorem,

  $\begin{array}{c}B{D}^2=A{D}^2+A{B}^2\\ x^2=8^2+8^2\\ x^2=64+64\\ x^2=128\end{array}$

Now, take square root of both sides,

  $\begin{array}{c}\sqrt{x^2}=\sqrt{128}\\ x=\sqrt{8\times 8\times 2}\\ x=8\sqrt{2}\end{array}$