In the adjoining figure, find AC.

GIVEN: In the figure we are given AD = 6cm, BD = 9cm, AE = 8cm

TO FIND: AC

According to BASIC PROPORTIONALITY THEOREM, if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

In ∆ABC, DE || BC. So,

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

$\frac{6}{9}=\frac{8}{\mathrm{EC}}$

$\mathrm{EC}=\frac{8 \times 9}{6}$

$\mathrm{EC}=12 \mathrm{~cm}$

Now,

$\mathrm{AC}=\mathrm{AE}+\mathrm{EC}$

$\mathrm{AC}=8+12$

$\mathrm{AC}=20 \mathrm{~cm}$