Question

In $△$ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.

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 $AD=6$ cm, $DB=9$ cm and $AE=8$ cm.

Using the basic proportionality theorem, we have

$\frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}\Rightarrow \frac{AD}{AB}=\frac{AE}{AC}\Rightarrow \frac{6}{15}=\frac{8}{AC}\Rightarrow 6AC=15\times 8\Rightarrow 6AC=120\Rightarrow AC=\frac{120}{6}=20$

Hence, $AC=20$ cm.