Question

In ∆ABC, DE ∥ BC so that AD = 2.4 cm, AE = 3.2 cm and EC = 4.8 cm. Then, AB = ?


(a) 3.6 cm
(b) 6 cm
(c) 6.4 cm
(d) 7.2 cm

Answer 1

(b) 6 cm

It is given that DE$\parallel$BC.

Applying basic proportionality theorem, we have:

$$\begin{gathered} \frac{AD}{BD}=\frac{AE}{EC} \\ \Rightarrow \frac{2.4}{BD}=\frac{3.2}{4.8} \\ \Rightarrow BD=\frac{2.4\times 4.8}{3.2}=3.6\mathrm{cm} \end{gathered}$$

Therefore, AB = AD + BD = 2.4 + 3.6 = 6 cm