Corresponding sides of two similar triangles are in the ratio of $ 2: 3 $. If the area of the smaller triangle is $ 48 \mathrm{~cm}^{2} $, find the area of the larger triangle.

Given: 

Corresponding sides of two similar triangles are in the ratio of \( 2: 3 \).

The area of the smaller triangle is \( 48 \mathrm{~cm}^{2} \).

To do: 

We have to find the area of the larger triangle.

Solution:

Given, ratio of corresponding sides of two similar triangles $=2:3$

$=\frac{2}{3}$

Area of smaller triangle $=48\ cm^2$

By the property of area of two similar triangles,

Ratio of area of both triangles$=\text{ (Ratio of their corresponding sides })^2 $

$\Rightarrow \frac{\text { area(smaller triangle) }}{\text { area(larger triangle) }}​=( \frac{2}{3})^2$

$\Rightarrow \frac{48}{\text { area( larger triangle) }}=\frac{4}{9}$

$\Rightarrow $Area of larger triangle $=\frac{48\times 9}{4}$

$=12\times9$

$=108\ cm^2$ 

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Updated on: 10-Oct-2022

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