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

Question:

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

Solution:

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.

$\therefore \frac{48}{\text { Area of larger triangle }}=\frac{2^{2}}{3^{2}}$

$\Rightarrow \frac{48}{\text { Area of larger triangle }}=\frac{4}{9}$

$\Rightarrow$ Area of larger triangle $=\frac{48 \times 9}{4}=108 \mathrm{~cm}^{2}$