Chapter 11.7, Problem 13WE

To determine

To Find: The name of similar triangles and find the ratio of their areas and find $DE$ .

Answer to Problem 13WE

  $\frac{ar(\Delta ABE)}{ar(\Delta DCE)}=\frac{36}{25}$

  $DE=\frac{40}{6}$

Explanation of Solution

Given:

  

Observe the figure

  $\begin{array}{l}\angle B=\angle C\\ \angle A=\angle D\\ thus\\ \Delta ABE\sim \Delta DCE\end{array}$

Now ratio of two sides $BEandCE$ is $6:5$ .

Then ratio of areas

  $6^2:5^2=36:25$

Now finding $DE$

Here the scale factor is $6:5$

Substitute $AE=8$

  $\begin{array}{l}\frac{AE}{DE}=\frac{6}{5}\\ \frac{8}{DE}=\frac{6}{5}\\ DE=\frac{40}{6}\end{array}$

Hence, $DE=\frac{40}{6}$ .