Question

$In\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{3}{5}.$ If $AC=5.6cm$, then $AE=$ _____.

• A. 2.1 cm
• B. 2.4 cm
• C. 3.2 cm
• D. 3.6 cm

Answer 1

The correct option is A

2.1 cm

$In\Delta ABC,DE||BC\left(Given\right)\frac{AD}{AB}=\frac{AE}{AC}\left[BasicProportionalityTheorem\right]$
$\because AB=(3+5),AD=3AC=5.6cm\left(Given\right)$

$\frac{3}{3+5}=\frac{AE}{5.6}$

$\frac{3}{8}=\frac{AE}{5.6}$

$AE=\frac{3\times 5.6}{8}=3\times 0.7=2.1cm$

$\Rightarrow AE=2.1cm$