Question

In the given figure, $DE\parallel BC$. If $AD=3.6cm,AB=9cm$ and $AE=2.4cm$, find $EC$

• A. $3.6cm$
• B. $8.9cm$
• C. $4.6cm$
• D. $3.9cm$

Answer 1

The correct option is A $3.6cm$

Given: AD = 3.6 cm, AB = 9 cm and AE = 2.4 cm $DE\parallel BC$
Since, $DE\parallel BC$, by Equal Intercept Theorem,
$\frac{AD}{BD}=\frac{AE}{EC}$
$\frac{AD}{AB-AD}=\frac{AE}{EC}$
$\frac{3.6}{9-3.6}=\frac{2.4}{EC}$
$EC=\frac{2.4\times 5.4}{3.6}$
$EC=3.6$ cm