2017 · Q92
In the figure given below, AC is parallel to ED and AB = DE = 5 cm and BC = 7 cm. What is the area ABDE : area BDE : area BCD equal to?
Elementary MathematicsQuadrilaterals and Polygons
- A10:5:7
- B8:4:7
- C2:1:2
- D8:4:5
Explanation
A, B, C are collinear with AC ∥ ED, so AB ∥ ED; with AB = DE = 5, ABDE is a parallelogram, and diagonal BD gives area(ABDE) = 2·area(ΔBDE). ΔBDE and ΔBCD share the altitude from D to line BC with bases BE:BC = 5:7, so area ABDE : area BDE : area BCD = 10:5:7: option A.