Question

Corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm², then the area of the larger triangle is _________.

Answer 1

We know that, the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

$$\begin{gathered} \therefore \frac{\mathrm{Area}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{\mathrm{Area}\mathrm{of}\mathrm{larger}\mathrm{triangle}}={\left(\frac{\mathrm{Length}\mathrm{of}\mathrm{corresponding}\mathrm{side}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{\mathrm{Length}\mathrm{of}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{larger}\mathrm{triangle}}\right)}^2 \\ \Rightarrow \frac{48{\mathrm{cm}}^2}{\mathrm{Area}\mathrm{of}\mathrm{larger}\mathrm{triangle}}={\left(\frac{2}{3}\right)}^2 \\ \Rightarrow \frac{48{\mathrm{cm}}^2}{\mathrm{Area}\mathrm{of}\mathrm{larger}\mathrm{triangle}}=\frac{4}{9} \\ \Rightarrow \mathrm{Area}\mathrm{of}\mathrm{larger}\mathrm{triangle}=\frac{48\times 9}{4}=108{\mathrm{cm}}^2 \end{gathered}$$

Corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm², then the area of the larger triangle is __108 cm²__.