Question

In a given $△ABC,DE||BC$ and $\frac{AD}{DB}=\frac{3}{5}$. If $AC=5.6$, find AE.

Answer 1

In $△ABC$, we have

$DE||BC$

$\therefore$ $\frac{AD}{DB}=\frac{AE}{EC}$ [By Thale's Theorem]

$\Rightarrow$ $\frac{AD}{DB}=\frac{AE}{AC-AE}$

$\Rightarrow$ $\frac{3}{5}=\frac{AE}{5.6-AE}$ $[\because AC=5.6]$

$\Rightarrow$ $3(5.6-AE)=5AE$

$\Rightarrow$ $16.8-3AE=5AE$

$\Rightarrow$ $8AE=16.8$

$\Rightarrow$ $AE=\frac{16.8}{8}cm=2.1$cm