Question

$\text{In the figure, PQ || AB. CQ = 4.8 cm,}\text{QB = 3.6 cm and AB = 6.3 cm. If AP = x,}\text{then what is the length of AC in terms of x ?}$

• A. $\frac{8}{3}xunits$
• B. $\frac{5}{3}xunits$
• C. $\frac{4}{3}xunits$
• D. $\frac{7}{3}xunits$

Answer 1

The correct option is D

$\frac{7}{3}xunits$

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

$PQ||AB\text{(Given)}$

$\text{By basic proportionality theorem,}\frac{CQ}{QB}=\frac{CP}{AP}\frac{4.8}{3.6}=\frac{CP}{AP}\frac{4}{3}=\frac{CP}{AP}$

Adding 1 both sides, we get

$\frac{4}{3}+1=\frac{CP}{AP}+1\frac{4+3}{3}=\frac{CP+AP}{AP}\frac{7}{3}=\frac{CP+AP}{AP}\frac{7}{3}=\frac{AC}{x}$
$AC=\frac{7}{3}xunits$