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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Given that the triangles are similar.
$\Rightarrow\frac{\text{area of the smaller triangle}}{\text{area of the larger triangle}}=\Big(\frac{2}{3}\Big)^2$
$\Rightarrow\frac{48}{\text{area of the larger triangle}}=\frac{4}{9}$
$\Rightarrow\text{area of the larger triangle = 108cm}^2$
$\Rightarrow\frac{\text{area of the smaller triangle}}{\text{area of the larger triangle}}=\Big(\frac{2}{3}\Big)^2$
$\Rightarrow\frac{48}{\text{area of the larger triangle}}=\frac{4}{9}$
$\Rightarrow\text{area of the larger triangle = 108cm}^2$
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