Diagonals of a trapezium PQRS intersect each other at the point 0, PQ || RS and PQ = 3 RS. Find the ratio of the areas of Δ POQ and Δ ROS.

Solution:

According to the given question,

The given figure, PQRS is a trapezium in which PQ || RS and PQ = 3RS

…(i)

In triangles POQ and ROS,

[vertically opposite angles]

[alternate angles]

∴ ∆POQ ∼ ∆ROS [using the AAA similarity criterion]

Using the property of area of similar triangle,

As a result, 9:1 is the required ratio.