Question:
In the adjoining figure, find AC.
Solution:
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,
$\mathrm{AC}=\mathrm{AE}+\mathrm{EC}$
$\mathrm{AC}=8+12$
$\mathrm{AC}=20 \mathrm{~cm}$