Corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller triangle is 48 cm2, then find the area of the larger triangle.
Given, ratio of corresponding sides of two similar triangles $=2: 3$ or $\frac{2}{3}$
Area of smaller triangle = 48 cm2
By the property of area of two similar triangle,
Ratio of area of both riangles = (Ratio of their corresponding sides)2
i.e., $\frac{\operatorname{ar}(\text { smaller triangle })}{\operatorname{ar}(\text { larger triangle })}=\left(\frac{2}{3}\right)^{2}$
$\Rightarrow$ $\frac{48}{\operatorname{ar}(\text { larger triangle })}=\frac{4}{9}$
$\Rightarrow$ ar (larger triangle) $=\frac{48 \times 9}{4}=12 \times 9=108 \mathrm{~cm}^{2}$
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