Question

In ∆ABC, DE is drawn parallel to BC, cutting AB and AC at D and E, respectively, such that AB = 7.2 cm, AC = 6.4 cm and AD = 4.5 cm. Find AE.


(a) 5.4 cm
(b) 4 cm
(c) 3.6 cm
(d) 3.2 cm

Answer 1

(b) 4 cm

It is given that DE$\parallel$BC.

Applying basic proportionality theorem, we get:

$$\begin{gathered} \frac{AD}{AB}=\frac{AE}{AC} \\ \Rightarrow \frac{4.5}{7.2}=\frac{AE}{6.4} \\ \Rightarrow AE=\frac{4.5\times 6.4}{7.2}=4\mathrm{cm} \end{gathered}$$