Question

If the area of two similar triangles is in the ratio $4:9$, then find the ratio of their corresponding sides

Answer 1

Find the ratio of the corresponding angles

We know that the ratio of the areas of two similar triangles will be equal to the square of the ratio of the corresponding sides

$$\begin{gathered} \therefore \frac{4}{9}={\left(\mathrm{Ratio}\mathrm{of}\mathrm{corresponding}\mathrm{sides}\right)}^2 \\ \Rightarrow \mathrm{Ratio}\mathrm{of}\mathrm{corresponding}\mathrm{sides}=\sqrt{\frac{4}{9}} \\ \Rightarrow \mathrm{Ratio}\mathrm{of}\mathrm{corresponding}\mathrm{sides}=\frac{2}{3} \end{gathered}$$

Hence the ratio is $2:3$