2016 · Q52
Suppose ABC is a triangle with AB of unit length. D and E are the points lying on AB and AC respectively such that BC and DE are parallel. If the area of triangle ABC is twice the area of triangle ABE, then the length of AD is
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1/2 unit
- B1/3 unit
- C1/(√(2)) unit
- D1/(√(3)) unit
Explanation
DE ∥ BC makes ΔADE ∼ ΔABC, so (AD/AB)² = area(ADE)/area(ABC) = 1/2. With AB = 1, AD = 1/√2, option C. (The official paper reads triangle ADE where the transcription says ABE.)