Chapter 11.7, Problem 14WE

To determine

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

Answer to Problem 14WE

  $\frac{ar(\Delta ACD)}{ar(\Delta ABE)}=\frac{100}{81}$

  $DE=8cm$

Explanation of Solution

Given:

  

Observe the figure

  $\begin{array}{l}\angle C=\angle E\\ \angle A=\angle A\\ thus\\ \Delta ACD\sim \Delta ABE\end{array}$

Now ratio of two sides $ADandAB$ is $10:9$ .

Then ratio of areas

  ${10}^2:9^2=100:81$

Now finding $DE$

Here the scale factor is $10:9$

Thus

  $DE=8cm$