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Question
In the figure below, PB and QA are perpendiculars to the line segment AB. If PO = 6 cm, QO = 9 cm and the area of ΔPOB = 120 cm2, find the area of ΔQOA.
Solution
PO = 6 cm, QO = 9 cm.
Area of ΔPOB = 120
In ΔPOB and ΔQOB,
∠B = ∠A ...(each 90°)
∠POB = ∠QOA ...(Opposite vertical angel)
∴ ΔPOB ∼ ΔQOA
In similar Δ's `"Area of ΔQOA"/"Area of ΔPOB" = "OQ"^2/"OP"^2`
`"Area of ΔQOA"/(120) = 9^2/6^2`
Area of ΔQOA = `(81 xx 120)/(36)`
= 27 x 10
Area of ΔQOA = 270 cm2.
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