Question

In the following figure, ray $AD$ is a bisector of $\angle BAC$. If $AB=4.8cm,BD=4cm$ and $DC=5cm$, find the value of $x$ (in $cm$).

Answer 1

In $\Delta ABD$ and $\Delta ACD$
$\therefore \angle BAD=\angle CAD$ ($\because AD$ is bisector of $\angle BAC$)
$\therefore AD=AD$
$\Delta ABD\sim \Delta ACD$
By Thales' theorem
$\frac{AB}{AC}=\frac{BD}{CD}$
Here, $AB=4.8cm,BD=4cm,CD=5cm,AC=x$
$\Rightarrow \frac{4.8}{x}=\frac{4}{5}$
$\Rightarrow x=\frac{4.8\times 5}{4}$
$\Rightarrow x=1.2\times 5=6.0cm$