2017 · Q65
In an equilateral triangle ABC, BD is drawn perpendicular to AC. What is BD² equal to ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AAD²
- B2AD²
- C3AD²
- D4AD²
Explanation
With side a: the altitude bisects the base, so AD = a/2, and BD² = AB²−AD² = a²−a²/4 = 3a²/4 = 3(a/2)² = 3AD². Hence option (C) 3AD².