ML Aggarwal Solutions Class 10 Mathematics Solutions for Similarity Exercise 13.3 in Chapter 13 - Similarity

Question 1 Similarity Exercise 13.3

In the figure, (i) given below, PB and QA are perpendiculars to the line segment AB. If PO = 6 cm, QO = 9 cm and the area of ∆POB = 120 cm², find the area of ∆QOA.



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

From the question it is given that, PO = 6 cm, QO = 9 cm and the area of ∆POB = 120 cm²

From the figure,

Consider the ∆AOQ and ∆BOP,

∠OAQ = ∠OBP … [both angles are equal to 90o]

∠AOQ = ∠BOP … [because vertically opposite angles are equal]

Therefore, ∆AOQ ~ ∆BOP

Then, area of ∆AOQ/area of ∆BOP = OQ2/PO2

Area of ∆AOQ/120 = 92/62

Area of ∆AOQ/120 = 81/36

Area of ∆AOQ = (81 × 120)/36

Area of ∆AOQ = 270 cm2 M L Aggarwal - Understanding ICSE Mathematics - Class 10 chapter Similarity Question 1 Solution image

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