2021 · Q26
In a trapezium ABCD, AB is parallel to DC. The diagonals AC and BD intersect at P. If AP ∶ PC = 4 ∶ (4x − 4) and BP ∶ PD = (2x − 1) ∶ (2x + 4), then what is the value of x?
Elementary MathematicsQuadrilaterals and Polygons
- A4
- B3
- C3/2
- D2
Explanation
The diagonals of a trapezium divide each other proportionally: AP/PC = BP/PD. So 4/(4x−4) = (2x−1)/(2x+4), which simplifies to 2x² − 5x − 3 = 0, i.e. (2x+1)(x−3) = 0. x = −1/2 would make segment lengths negative, so x = 3. Hence option B.