In ΔABC, DE is drawn parallel to BC cutting the other two sides at D and E. If AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm, then AE is equal to:

1. 1.05 cm

2. 1.2 cm

3. 1.4 cm

4. 1.8 cm

Given,

In ΔABC and ΔADE,

∠A = ∠A [Common angle]

∠ABC = ∠ADE [Corresponding angles are equal]

∴ ΔABC ∼ ΔADE (By A.A. axiom).

We know that,

Corresponding sides of similar triangle are proportional.

$\Rightarrow \dfrac{AB}{AD} = \dfrac{AC}{AE} \\[1em] \Rightarrow \dfrac{3.6}{2.1} = \dfrac{2.4}{AE} \\[1em] \Rightarrow AE = \dfrac{2.4 \times 2.1}{3.6} \\[1em] \Rightarrow AE = \dfrac{5.04}{3.6} \\[1em] \Rightarrow AE = 1.4 \text{ cm.}$

Hence, option 3 is the correct option.