Chapter E, Problem 11.8EX

To determine

To find: The ratio of the areas of $\Delta AOB$ and $\Delta AOD$ .

Answer to Problem 11.8EX

The ratio of the areas of $\Delta AOB$ and $\Delta AOD$ is $324:100$ .

Explanation of Solution

Given information:

The given figure is,

  

The second side of $\Delta AOB$ is 18.

The second side of $\Delta AOD$ is 10.

Calculation:

The two sides of triangle $\Delta AOB$ and $\Delta AOD$ sides are same as 10.

Calculate the ratio of the areas of the triangles.

  $\begin{array}{c}Area=\frac{\Delta {\rm A}{\rm O}{\rm B}}{\Delta AOD}\\ =\frac{A{B}^2}{A{D}^2}\\ =\frac{{\left(18\right)}^2}{{\left(10\right)}^2}\\ =\frac{324}{100}\end{array}$

Therefore, the ratio of the areas of $\Delta AOB$ and $\Delta AOD$ is $324:100$ .