Question

In $\Delta ABC$, $DE$ is parallel to $BC$ and $\frac{AD}{DB}=\frac{2}{7}$. If $AC$=$5.6$, find $AE$ .

Answer 1

Step: Find AE

Given:$DE\left|\right|BC$,$\frac{AD}{DB}=\frac{2}{7}$ and $AC$=$5.6$.
Let us assume that $AE$ =$y$
In $△ABC$, $DE\left|\right|BC$
$\therefore \frac{AD}{DB}=\frac{AE}{EC}$ [$\therefore$ A line drawn parallel to one side of a triangle divides the other two sides proportionally (BPT) ]
$\Rightarrow \frac{2}{7}=\frac{y}{(5.6-y)}$
$\Rightarrow 2(5.6-y)=7y$
$\Rightarrow y=\frac{11.2}{9}=1.24$
$\therefore$ $AE$ is $1.24$