Discussion

Question:

PQRS is a trapezium in which the length of the parallel sides PQ and RS is in the ratio 3 : 4. If the diagonals intersect at O, then find the ratio of area of ΔPOQ to ΔROS.

Explanation:

In ∆POQ and ∆ROS
∠OPQ = ∠ORS (Corresponding angles)
∠OQP = ∠OSR (Corresponding angles)

∴ ∆POQ ~ ∆ROS

⇒ $fraction numerator A r e a space o f space increment P O Q over denominator A r e a space o f space increment S O R end fraction equals open parentheses fraction numerator P Q over denominator S R end fraction close parentheses squared equals open parentheses fraction numerator 3 x over denominator 4 x end fraction close parentheses squared equals 9 over 16$

(Since triangles are similar.)

Hence, option (b).

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