In the given Fig. PB and QA are perpendiculars to segment AB. If PO = 5 cm, QO = 7 cm and area ∆POB = 150 cm² find the area of ∆QOA.

In ∆OAQ and ∆OBP, we have
∠A = ∠B [Each equal to 90°]
∠AOQ = ∠BOP [Vert.opp.angles]
Therefore by using AA similar condition, we have
$increment AOQ space equals space increment BOP$
$space space rightwards double arrow space space space space space space space fraction numerator Area left parenthesis increment AOQ right parenthesis over denominator Area left parenthesis increment BOP right parenthesis end fraction equals OQ squared over OP squared$
$rightwards double arrow$ $fraction numerator Area left parenthesis increment AOQ right parenthesis over denominator 150 end fraction equals 7 squared over 5 squared$

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In the given Fig. PB and QA are perpendiculars to segment AB. If PO = 5 cm, QO = 7 cm and area ∆POB = 150 cm2 find the area of ∆QOA.

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Mathematics

In the given Fig. PB and QA are perpendiculars to segment AB. If PO = 5 cm, QO = 7 cm and area ∆POB = 150 cm² find the area of ∆QOA.