# Solve this

Question:

In $\Delta A B C, D E \| B C$ such that $\frac{A D}{D B}=\frac{3}{5}$.

If AC = 5.6 cm, then AE = ?

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

Solution:

(d) 2.1 cm

It is given that $\mathrm{DE} \| B C$.

Applying Thales' theorem, we get:

$\frac{A D}{D B}=\frac{A E}{E C}$

Let $A E$ be $x \mathrm{~cm}$.

Therefore, $E C=(5.6-x) \mathrm{cm}$

$\Rightarrow \frac{3}{5}=\frac{x}{5.6-x}$

$\Rightarrow 3(5.6-x)=5 x$

$\Rightarrow 16.8-3 x=5 x$

$\Rightarrow 8 x=16.8$

$\Rightarrow x=2.1 \mathrm{~cm}$