# 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.

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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 $=\frac{48\times 9}{4}$

$=12\times9$

$=108\ cm^2$

Updated on 10-Oct-2022 13:28:05