In the figure below, PB and QA are perpendiculars to segment AB. If PO = 5 cm, QO = 7 cm and area ∆POB = 150 sq.cm., find area of ∆QOA.
Explanation:
In ∆PBO and ∆QAO
∠B = ∠A = 90°
∠POB = ∠QOA (vertically opposite angles)
∴ ∆PBO ∼ ∆QAO ...(By A-A test of similarity)
⇒ The ratio of the areas of similar triangles is equal to ratio of the square of the their respective sides.
⇒ POQO2=Area∆PBOArea∆QAO
⇒ 572=150Area∆QAO
⇒ Area(∆QAO) = 294 sq.cm.
Hence, 294.
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