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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