Question

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

Answer 1

In triangles AOQ and BOP, we have

$\angle OAQ=\angle OBP$ [Each equal to ${90}^{\circ }$]

$\angle AOQ=\angle BOP$ [Vertically opposite angles]

Therefore, by AA-criterion of similarity

$△AOQ\sim △BOP$

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

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

$\Rightarrow$ $\frac{10}{6}=\frac{AQ}{9}$

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