Question

Diagonals of a trapezium PQRS intersect each other at the point O. If PQ || RS and PQ = 3RS, then `(ar(ΔPOQ))/(ar(ΔROS))` = ______.

Answer 1

Diagonals of a trapezium PQRS intersect each other at the point O. If PQ || RS and PQ = 3RS, then `(ar(ΔPOQ))/(ar(ΔROS))` = 9.

Explanation:

In triangles POQ and ROS, ∠QOP = ∠SOR (vertically opposite) and corresponding angles formed by PQ || RS are equal, so the triangles are similar (AA).

Hence the ratio of their areas equals the square of the ratio of corresponding sides: `(PQ)/(RS^2) = 3^2 = 9`.