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

Given: Corresponding sides of two similar triangles are in the ratio of $2 : 3$. If the area of the smaller triangle is $48 cm \ 2$

To do: To find the area of the larger triangle is:

Solution:

Given, ratio of corresponding sides of two similar triangles $=2:3$ or $\frac{2}{3}$

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

By the property of area of two similar triangle,

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

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

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

$\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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