Question

In $\Delta ABC,D$ and $E$ are points on sides AB and AC respectively such that DE $\parallel$ BC and $AD:DB=3:1$ If $EA=6.6cm$ then find $AC$

Answer 1

Given $AD/BD=3/1$

Using Basic proportionality theorem, In a triangle a line is drawn parallel to one side of a triangle and intersect the other two side at distinct points, the other two sides are divided in the same ratio.

In $\Delta ABC\Rightarrow \frac{AD}{BD}=\frac{AE}{EC}\Rightarrow \frac{3}{1}=\frac{6.6}{EC}\Rightarrow EC=2.2$

Now $AC=AE+EC$

$AC=6.6+2.2=8.8$ cm