Question

Diagonals of a trapezium PQRS intersect each other at the point 0 ,PQ`abs()`RS and PQ=3 RS. Find the ratio of the areas of `DeltaPOQ` and `DeltaROS`.

Answer 1

Here PQRS is a trapezium in which PQ||RS and PQ = 3RS. In `trianglePOQ and triangleROS`
` angleOPQ = angleORS` (alternate angles)
`angleOQP = angleOSR` (alternate angles)
`trianglePOQ~ triangleROS` ( AA similarity)
`(area(trianglePOQ))/(area(triangleROS))= (PQ^(2))/(RS^(2))`
` ((3RS)^(2))/(RS^(2))= 9/1 = 9:1`