Question

In $\Delta ABC,DE||BC$ and $\frac{AD}{DB}=\frac{3}{4}$ and AC=28 cm then AE is (image)

• A. 21 cm
• B. 12 cm
• C. 16 cm
• D. 24 cm

Answer 1

Answer: (B)

12 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, $\frac{AD}{AB}=\frac{AE}{AC}⟹\frac{3}{7}=\frac{AE}{28}⟹AE=12$.