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Question

In the figure given below, sides PB and QA are perpendiculars drawn to the line segment AB.
If PO = 6 cm, QO = 9 cm, and area of ΔPOB=120 cm2, then find the area of ΔQOA.


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Solution

In ΔPOB and ΔQOA,

PBO=QAO=90

POB=QOA
(Since vertically opposite angles are equal)

ΔPOB ΔQOA
(by AA similarity criterion)

ar(ΔPOB)ar(ΔQOA)=PO2QO2

(The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides).

120ar(QOA)=6292

ar(QOA)=120×8136=270 cm2


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