Question

$ABC$ is a triangle and $DE$ is drawn parallel to $BC$ cutting the other sides at $D$ and $E$. If $AB=3.6cm,AC=2.4cm$ and $AD=2.1cm$, then $AE$ = ______.

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

Answer 1

The correct option is A $1.4cm$

By Basic Proportionality Theorem,
$\frac{BD}{AD}=\frac{CE}{AE}$
$\frac{BD}{AD}+1=\frac{CE}{AE}+1$
$\frac{AD+BD}{AD}=\frac{AE+CE}{AE}$
$\frac{AB}{AD}=\frac{AC}{AE}$
Subtituting values:
$\frac{3.6}{2.1}=\frac{2.4}{AE}$
$AE=\frac{2.1\times 2.4}{3.6}=1.4cm$