2021 · Q19
ABCD is a trapezium in which AB is parallel to DC and 2AB = 3DC. The diagonals AC and BD intersect at O. What is the ratio of the area of ΔAOB to that of ΔDOC?
Elementary MathematicsQuadrilaterals and Polygons
- A2 ∶ 1
- B3 ∶ 2
- C4 ∶ 1
- D9 ∶ 4
Explanation
Since AB ∥ DC, △AOB ∼ △DOC with linear ratio AB/DC = 3/2 (from 2AB = 3DC). The ratio of areas of similar triangles is the square of the linear ratio: (3/2)² = 9/4. Hence option D.