Question

In the figure given below, point D divides AB in the ratio 3 : 5 and DE is parallel to BC. If $AE=4.8$ cm, then find the length of AC.

Answer 1

In $\Delta$ABC,
DE || BC (Given)
Since point D divides AB in the ratio 3 : 5.
So, AD : DB = 3 : 5
By basic proportionality theorem,
$\frac{AD}{DB}=\frac{AE}{EC}$
$\frac{3}{5}=\frac{4.8}{EC}$
$EC=\frac{4.8\times 5}{3}$
$\Rightarrow EC=8$
Now, $AC=AE+EC$
$\Rightarrow AC=4.8+8=12.8$ cm