Question

In $\Delta ABC,DE||BC$ and $\frac{AD}{BD}=\frac{3}{2}$ and EC = 3 then AE is

• A. 4.5 cm
• B. 7.5 cm
• C. 6 cm
• D. 3.5 cm

Answer 1

The correct option is D 3.5 cm

In $\Delta ADEand\Delta ABC,\angle Aiscommon,\angle ADE=$

$\angle ABCand\angle AED=\angle ACB\left[correspondinganglepairs\right]$
Hence the triangles are similar by AAA.
So, $\frac{AD}{AB}=\frac{AE}{AC}⟹\frac{3}{5}=\frac{AE}{AE+3}$.
$⟹\frac{3}{5}=\frac{AE}{AE+3}⟹3AE+9=5AE⟹9=2AE⟹AE=4.5$