2026 · Q54
Let ABCD be a parallelogram and E be the midpoint of BC. The diagonal BD and line segment AE intersects at F. If BF = 2.4 cm, then what is BD equal to?
Elementary MathematicsQuadrilaterals and Polygons
- A6.0 cm
- B6.4 cm
- C7.2 cm
- D8.4 cm
Explanation
ΔBFE is similar to ΔDFA (alternate interior angles), and since E is the midpoint of BC, BE/AD=1/2. Thus BF/FD=1/2, so FD=2×2.4=4.8 cm and BD=2.4+4.8=7.2 cm, option C. The similarity ratio 1:2 comes from E being the midpoint of BC in a parallelogram, where AD=BC.