Question

In $△$ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 8 cm, AB = 12 cm, AE = 12 cm, find CE.

Answer 1

The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

It is given that $AD=8$ cm, $AB=12$ cm and $AE=12$ cm.

Using the basic proportionality theorem, we have

$\frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}\Rightarrow \frac{AD}{AB}=\frac{AE}{AC}\Rightarrow \frac{8}{12}=\frac{12}{AC}\Rightarrow 8AC=12\times 12\Rightarrow 8AC=144\Rightarrow AC=\frac{144}{8}=18$

Now, $CE=AC-AE=18-12=6$ cm

Hence, $CE=6$ cm.