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Question 4
Diagonals of a trapezium PQRS intersect each other at the point O, PQIIRS and PQ = 3 RS. Find the ratio of the areas of ΔPOQ and ΔROS.

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Solution

Given PQRS is a trapezium in which PQ II RS and PQ = 3RS.
PQRS=31 ....(i)

In ΔPOQ and ΔROS,
SOR=QOP [vertically opposite angles]
SRP=RPQ [ alternate angles]
ΔPOQΔROS [by AAA similarity criterion]
By property of area of similar triangle,
ar(ΔPOQ)ar(ΔROS)=(PQ)2(RS)2=(PQRS)2=(31)2 [from Eq. (i)]
ar(ΔPOQ)ar(ΔROS)=91
Hence, the required ratio is 9:1.

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