The corresponding sides of two similar triangles are in the ratio $2 : 3$. If the area of the smaller triangle is $48\ cm^2$, find the area of the larger triangle.
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It is given that the triangles are similar.
Therefore, the ratio of areas of similar triangles will be equal to the ratio of squares of their corresponding sides.
$\therefore\frac{48}{\text{Area of larger triangle}}=\frac{2^2}{3^2}$
$\Rightarrow\frac{48}{\text{Area of larger triangle}}=\frac{4}{9}$
$\Rightarrow\text{Area of larger triangle}=\frac{48\times9}{4}=108\text{cm}^2$
Therefore, the ratio of areas of similar triangles will be equal to the ratio of squares of their corresponding sides.
$\therefore\frac{48}{\text{Area of larger triangle}}=\frac{2^2}{3^2}$
$\Rightarrow\frac{48}{\text{Area of larger triangle}}=\frac{4}{9}$
$\Rightarrow\text{Area of larger triangle}=\frac{48\times9}{4}=108\text{cm}^2$
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