Question

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

Answer 1

Given that AD/BD=3/1

in ΔABC

AD/BD=AE/EC

3/1=6.6/EC

EC=2.2

NOW AC=AE+EC

AC=6.6+2.2

AC=8.8

Answer 2

Answer:

AC=8.8 cm

Explanation:

In ΔABC, D and E are the points on sides AB and AC respectively such that DE parallel to BC as shown in attach figure.

AD:DB=3:1 or $\frac{AD}{DB}=\frac{3}{1}$

If EA=6.6 cm

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.

$\therefore \frac{AD}{DB}=\frac{AE}{EC}$

Substitute the value of AD:DB and AE. We get

$\frac{3}{1}=\frac{6.6}{EC}$

EC=2.2 cm

We need to find length of AC.

AC=AE+EC

AC=6.6+2.2

AC=8.8 cm