Question

In the given figure, $QA$ and $PB$ are perpendiculars to $AB.$ If $AO=10$ cm, $BO=6$ cm and $PB=9$ cm, find $AQ.$

• A. $5$ cm
• B. $10$ cm
• C. $15$ cm
• D. $20$ cm

Answer 1

Answer: (C)

$15$ cm

In $△$ $AOQ$ and $△BOP$, we have

$\angle OAQ=\angle OBP$ (Each equal to ${90}^{\circ }$)

$\angle AOQ=\angle POB$ (Vertically opp. $\angle$s)

$\therefore$ By AA-similarity,

$△AOQ\sim △BOP$

$\Rightarrow$ $\frac{AO}{BO}=\frac{OQ}{OP}=\frac{AQ}{BP}$

$\frac{AO}{BO}=\frac{AQ}{9}=\frac{10}{6}\Rightarrow AQ=\frac{10\times 9}{6}=15cm$