Chapter 11.7, Problem 27WE

To determine

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

Answer to Problem 27WE

  $\frac{9}{40}$

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 $ACandAD$ is

  $\frac{a}{b}=\frac{7}{3}$

Then ratio of areas

  $\frac{a^2}{b^2}=\frac{7^2}{3^2}=\frac{49}{9}$

Now

  $\begin{array}{l}\frac{ar(II)}{ar(I)}=\frac{49}{9}-1\\ \frac{ar(II)}{ar(I)}=\frac{40}{9}\\ \frac{ar(I)}{ar(II)}=\frac{9}{40}\end{array}$

Hence $\frac{ar(I)}{ar(II)}=\frac{9}{40}$ .