Question

In $\Delta ABC,AB=16cm,BC=9.6cm.CD\perp AB$ and $AE\perp BC$. If CD = 6 cm, the find the length of AE.

Answer 1

Area of $\Delta ABC=\frac{1}{2}\times AB\times DC$
$=\frac{1}{2}\times 16\times 6$
$=16\times 3=48c{m}^2$
Area of $\Delta ABC$ can also be written as $\frac{1}{2}\times BC\times AE$
$\Rightarrow \frac{1}{2}\times BC\times AE=48$
$\Rightarrow \frac{1}{2}\times 9.6\times AE=48$
$\Rightarrow AE=\frac{48\times 2}{9.6}=\frac{96}{9.6}=10cm$