Areas of two similar triangles are $ 36 \mathrm{~cm}^{2} $ and $ 100 \mathrm{~cm}^{2} $. If the length of a side of the larger triangle is $ 20 \mathrm{~cm} $, find the length of the corresponding side of the smaller triangle.

Given: 

Areas of two similar triangles are $36\ cm^2$ and $100\ cm^2$. If the length of a side of the larger triangle is $20\ cm$.

To do: 

We have to find the length of the corresponding side of the smaller triangle.

Solution:

As given, area of smaller triangle $=36\ cm^2$

Area of larger triangle $=100\ cm^2$

Length of the side of the larger triangle $=20\ cm$

Let $x\ cm$ be the length of the corresponding side of the smaller triangle.

We know that,

$\frac{\text { area( larger triangle) }}{\text { area( smaller triangle) }}=\frac{\text { (side of larger triangle })^2}{\text { (side of smaller triangle })^2}$

$\Rightarrow \frac{36}{100}=(\frac{x}{20})^2$

$\Rightarrow \frac{6^2}{10^2}=(\frac{x}{20})^2$

$\Rightarrow (\frac{6}{10})^2=(\frac{x}{20})^2$

$\Rightarrow \frac{6}{10}=\frac{x}{20}$

$\Rightarrow x=2\times6$

$\Rightarrow x=12$

Hence, the corresponding side of the smaller triangle is $12\ cm$.