Question

In $\Delta ABC$, AC = 15 cm and DE || BC. If $\frac{AD}{DB}=\frac{1}{2}$, then AE=___

• A. 5 cm
• B. 10 cm
• C. 7.5 cm
• D. 12.5 cm

Answer 1

The correct option is A 5 cm

Given: AC = 15 cm
DE$\parallel$ BC
$\frac{AD}{DB}=\frac{1}{2}$
In $\Delta$ ADE and $\Delta$ ABC,
$\angle DAE$ = $\angle BAC$ [ Common ]
$\angle ADE$ = $\angle ABC$ and $\angle AED$ = $\angle ACB$
[ $\because$ DE$\parallel$ BC, corresponding angles are equal ]
$\Rightarrow$ $\Delta ADE$ ∼ $\Delta ABC$ [AA similarity]
From Basic Proportionality theorem,
$\frac{AD}{DB}=\frac{AE}{EC}$
$\Rightarrow \frac{AE}{EC}=\frac{1}{2}\Rightarrow EC=2AEAC=15cm\Rightarrow AE+EC=15cm\Rightarrow 3AE=15cm\Rightarrow AE=5cm$