2026 · Q70
In a triangle ABC, AB = 8 cm and D and E are points on AB and AC respectively such that DE is parallel to BC. If BC = 5DE, then what is AD × BD equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A10 cm²
- B10.24 cm²
- C10.56 cm²
- D12 cm²
Explanation
Since DE ∥ BC, ΔADE ∼ ΔABC with linear ratio DE/BC = 1/5. Thus AD/AB = 1/5, giving AD = 8/5 = 1.6 cm and BD = 8 − 1.6 = 6.4 cm. Their product is 1.6 × 6.4 = 10.24 cm², option B.