In given figure, PB and QA are perpendiculars to segment AB. If PO=5 cm, QO=7 cm and Area △POB=150cm 2 find the area of △QOA

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In the given figure we have been asked to find the area of ΔQOA, if PB and QA are perpendiculars to segment AB. If PO=5 cm, QO=7 cm and Area △POB=150cm2

ML Aggarwal Avichal Publication class 10, Similarity, chapter 13.3, question no 5a

## In △OAQ and △OBP, we have ∠A=∠B [Each equal to 90∘] ∠AOQ=∠BOP

## So, by AA-criterion of similarity, we have △AOQ∼△BOP

⇒ Area(BOP)/Area(△AOQ)=OP^2/OQ^2

⇒ 150/Area(△AOQ)=5^2/7^2

⇒ Area(△AOQ)=49/25×150cm2

=294cm2