Question

In a given $\Delta ABC,DE\parallel BC$ and $\frac{AB}{DB}=\frac{3}{5}$. If AC = 5.6, find AE. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

In $\Delta ABC$, we have

$DE\parallel BC$

$\therefore \frac{AD}{DB}=\frac{AE}{EC}$ [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]

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

$\Rightarrow 16.8-3AE=5AE$

$\Rightarrow 8AE=16.8$

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