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] ∴ΔPOQ∼ΔROS [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.