Question

In triangle ABC, points D and E lie on sides AB and AC respectively such that DE is parallel to BC.

If AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm, then AE is equal to ____.

• A. $1.8cm$
• B. $1.05cm$
• C. $1.2cm$
• D. $1.4cm$

Answer 1

The correct option is D

$1.4cm$

$\text{In}\Delta ADE\text{and}\Delta ABC,DE||BC\text{(Given)}$

$\angle ADE=\angle ABC\text{(Pair of corresponding angles)}$

$\angle AED=\angle ACB\text{(Pair of corresponding angles)}$

$\therefore \Delta ADE\sim \Delta ABC\text{(AA similarity criterion)}$

$\frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}\text{(Corresponding sides of similar}\text{triangles are proportional)}$

$\Rightarrow \frac{AD}{AB}=\frac{AE}{AC}$

$\Rightarrow$ $\frac{2.1}{3.6}=\frac{AE}{2.4}$

$AE=\frac{2.1\times 2.4}{3.6}=1.4cm$