Question

$\text{In the figure, PQ || AB, CQ = 6 cm,}\text{CB = 8 cm. If CP = 7 cm,}\text{then what is the length of AC?}$

• A. $8cm$
• B. $9cm$
• C. $\frac{25}{4}cm$
• D. $\frac{28}{3}cm$

Answer 1

The correct option is D $\frac{28}{3}cm$

$\text{In}\Delta CQP\text{and}\Delta CBA,$

$PQ||AB\text{(Given)}$
$\because \angle ACB=\angle PCQ$ and $\angle ABC=\angle PQC$
$\therefore \Delta CQP\cong \Delta CBA$

$\text{By basic proportionality theorem,}\frac{CQ}{CP}=\frac{CB}{CA}\Rightarrow \frac{6}{7}=\frac{8}{CA}$

Cross multiply
$\Rightarrow 6\times CA=7\times 8$
$\Rightarrow 6\times CA=56\Rightarrow CA=\frac{56}{6}=\frac{28}{3}cm$