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.

Answer 1

In Δs AOQ and BOP, we have

∠OAQ = ∠OBP        (Each equal to 90°) 

∠AOQ = ∠POB        (Vertically opp.∠s) 

∴ By AA–similarity, 

ΔAOQ ~ ΔBOP

⇒ \(\frac{AO}{BO}=\frac{OQ}{OP}=\frac{AQ}{BP}\)

⇒ \(\frac{AO}{BO}=\frac{AQ}{BP}\) ⇒ \(\frac{10}{6}=\frac{AQ}{9}⇒AQ=\frac{10\times9}{6} = 15 cm.\)