Chapter 14.4, Problem 5MRE

To determine

To find: Ratio of areas of $\Delta OBC$ to $\Delta ODE$ .

Answer to Problem 5MRE

Ratio of areas of $\Delta OBC$ to $\Delta ODE$ is $4:9$ .

Explanation of Solution

Given information :

  $\overline{ED}\left|\right|\overline{BC}\left|\right|\overline{FG}$

Concept used:

If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides.

As per the given problem

Following diagram is provided.

  

Given: $\overline{ED}\left|\right|\overline{BC}\left|\right|\overline{FG}$

  $\Delta OBC$ similar to $\Delta ODE$ .

  $\begin{array}{l}\frac{OB}{OD}=\frac{BC}{DE}=\frac{CO}{EO}\\ \Rightarrow \frac{BC}{DE}=\frac{2}{3}\end{array}$

  $\frac{ar(\Delta OBC)}{ar(\Delta ODE)}=\frac{B{C}^2}{D{E}^2}={(\frac{BC}{DE})}^2$

  $\Rightarrow {(\frac{2}{3})}^2=\frac{4}{9}$

Hence,

Ratio of areas of $\Delta OBC$ to $\Delta ODE$ is $4:9$ .