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.

Answer 1

If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
$$\begin{gathered} \therefore \frac{\mathrm{area}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{\mathrm{area}\mathrm{of}\mathrm{larger}\mathrm{triangle}}={\left(\frac{\mathrm{Side}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{\mathrm{Side}\mathrm{of}\mathrm{larger}\mathrm{triangle}}\right)}^2 \\ \Rightarrow \frac{48}{\mathrm{area}\mathrm{of}\mathrm{larger}\mathrm{triangle}}={\left(\frac{2}{3}\right)}^2 \\ \Rightarrow \mathrm{area}\mathrm{of}\mathrm{larger}\mathrm{triangle}=108{\mathrm{cm}}^2 \end{gathered}$$