Question

If $DE\parallel BC$ in $△ABC,AD=1.5cm,BD=3cm$ and $AE=1cm$, then find $EC$ ( in cm ).

Answer 1

The given information is shown in the attached diagram.

$DE||BC$

$⟹\angle ADE=\angle ABC$ Corresponding angles

$\angle AED=\angle ACB$ Corresponding angles

$\angle A$ is common to both the triangles.

$\therefore \Delta ADE\sim \Delta ABC$ by $AAA$ similarity

$⟹\frac{AB}{AD}=\frac{AC}{AE}$

$\frac{AB}{AD}-1=\frac{AC}{AE}-1$

$\frac{BD}{AD}=\frac{CE}{AE}$

$EC=1\times \frac{3}{1.5}=2cm$