2012 · Q15
In the triangle ABC, the base BC is trisected at D and E. The line through D, parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. Let EG and DF intersect at H. What is the ratio of the sum of the area of parallelogram AGHF and the area of the triangle DHE to the area of the triangle ABC?
Elementary MathematicsGeometry
- A1/2
- B1/3
- C1/4
- D1/6
Explanation
With A=(0,0), B=(3,0), C=(0,3): F=(0,1), G=(1,0), H=(1,1). Parallelogram AGHF has area 1 and triangle DHE has area 1/2, while triangle ABC has area 9/2; the ratio is (3/2)/(9/2) = 1/3.