Question

In $\Delta ABC,DE//BC$ and AC = 5.6 cm, AE = 2.1 cm then find AD : DB.

Answer 1

Since $DE||BC$

$\therefore \angle ADE=\angle ABC$ [parallel lines cut by transversal]

& $\angle AED=\angle ACB$

In $\Delta ABC$ & $\Delta ADE$

$\Rightarrow \angle A=\angle A$ [common angle]

$\Rightarrow \angle ADE=\angle ABC$

$\Rightarrow AED=\angle ACB$

By AAA, $\Delta ABC\sim \Delta ADE$

So $\frac{AE}{AC}=\frac{AD}{AB}=\frac{2.1}{5.6}$

$DB=AB-AD=5.6-2.1=3.5$

So $\frac{AD}{DB}=\frac{2.1}{3.5}=\frac{3}{5}$.