Chapter 11.7, Problem 26WE

To determine

To Find: The ratio of area of $IandII$ .

Answer to Problem 26WE

  $1:10$

Explanation of Solution

Given:

  

  

  $\begin{array}{l}\angle ABC=\angle DEA\\ \angle A=\angle A\\ Thus\\ \Delta BCA\sim \Delta EAD\end{array}$

The ratio of sides $ACandAE$ is

  $\frac{a}{b}=\frac{18}{8}$

Then ratio of areas

  $\frac{a^2}{b^2}=\frac{{18}^2}{8^2}=\frac{324}{64}=\frac{81}{16}$

Now

  $\begin{array}{l}\frac{ar(II)}{ar(I)}=\frac{18}{8}-1\\ \frac{ar(II)}{ar(I)}=\frac{80}{8}=10:1\\ \frac{ar(I)}{ar(II)}=\frac{1}{10}\end{array}$

Hence $1:10$ .