The ratio of the corresponding sides of the two similar triangles is 2:3 and the area of the smaller triangle is 24 sq. cm. Find the area of the bigger triangle.

Let ΔABC and ΔPQR be two similar triangles as shown below.

Let the area of the smaller triangle ABC be 24 sq. cm.

We need to find the area of the bigger ΔPQR.

We know that the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.

$\therefore \frac{\mathrm{Area} \mathrm{of} △\mathrm{ABC}}{\mathrm{Area} \mathrm{of} △\mathrm{PQR}}=\frac{2^2}{3^2}$

$\Rightarrow \frac{24}{\mathrm{Area} \mathrm{of} △\mathrm{PQR}}=\frac{4}{9}$

$\Rightarrow \mathrm{Area} \mathrm{of} △\mathrm{PQR}=\frac{24\times 9}{4}=54 \mathrm{sq}. \mathrm{cm}$

Hence, the area of the bigger ΔPQR is 54 sq. cm.