Question

In $∆ABC,DE\parallel BC\mathrm{such}\mathrm{that}\frac{AD}{DB}=\frac{3}{5}.$
If AC = 5.6 cm, then AE = ?


(a) 4.2 cm
(b) 3.1 cm
(c) 2.8 cm
(d) 2.1 cm

Answer 1

(d) 2.1 cm

It is given that DE$\parallel BC$.
Applying Thales' theorem, we get:
$$\begin{gathered} \frac{AD}{DB}=\frac{AE}{EC} \\ \mathrm{Let}AE\mathrm{be}x\mathrm{cm}. \\ \mathrm{Therefore},EC=\left(5.6-x\right)\mathrm{cm} \\ \Rightarrow \frac{3}{5}=\frac{x}{5.6-x} \\ \Rightarrow 3(5.6-x)=5x \\ \Rightarrow 16.8-3x=5x \\ \Rightarrow 8x=16.8 \\ \Rightarrow x=2.1\mathrm{cm} \end{gathered}$$