Question

In the given figure, DE ∥ BC. If DE = 3 cm, BC = 6 cm and ar(∆ADE) = 15 cm², find the area of ∆ABC.

Answer 1

It is given that DE ∥ BC

$$\begin{gathered} \therefore \angle ADE=\angle ABC(\mathrm{Corresponding}\mathrm{angles}) \\ \angle AED=\angle ACB(\mathrm{Corresponding}\mathrm{angles}) \end{gathered}$$

By AA similarity , we can conclude that $△ADE~△ABC$.

$$\begin{gathered} \therefore \frac{\mathrm{ar}(∆ADE)}{\mathrm{ar}(∆ABC)}=\frac{D{E}^2}{B{C}^2} \\ \Rightarrow \frac{15}{\mathrm{ar}(∆ABC)}=\frac{3^2}{6^2} \\ \Rightarrow \mathrm{ar}(∆ABC)=\frac{15\times 36}{9} \\ =60{\mathrm{cm}}^2 \end{gathered}$$

Hence, area of triangle ABC is 60 cm².​