The corresponding sides of two similar triangles are in the ratio of 2 : 3.

Question:

The corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller triangle is 48 cm2 , find the area of larger triangle.

Solution:

If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

$\therefore \frac{\text { area of smaller triangle }}{\text { area of larger triangle }}=\left(\frac{\text { Side of smaller triangle }}{\text { Side of larger triangle }}\right)^{2}$

$\Rightarrow \frac{48}{\text { area of larger triangle }}=\left(\frac{2}{3}\right)^{2}$

$\Rightarrow$ area of larger triangle $=108 \mathrm{~cm}^{2}$