2022 · Q100
In a triangle ABC, DE is a line segment which intersects AB at D and AC at E such that DE is parallel to BC. The line segment divides the triangle in two parts of equal area. What is (BD)/(AB) equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2-12
- B2-12
- C3-13
- D√2
Explanation
ΔADE ∼ ΔABC with area ratio 1/2, so AD/AB = 1/√2. Hence BD/AB = 1−1/√2 = (√2−1)/√2. (Options A and B lost their fraction formatting in digitisation; the value (√2−1)/√2 is the keyed one.) The keyed option is B.