2017 · Q82
One-fifth of the area of a triangle ABC is cut off by a line DE drawn parallel to BC such that D is on AB and E is on AC. If BC = 10 cm, then what is DE equal to ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A√(5) cm
- B2√(5) cm
- C3√(5) cm
- D4√(5) cm
Explanation
△ADE ∼ △ABC with DE ∥ BC. Area ratio 1/5 gives linear ratio 1/√5, so DE = 10/√5 = 2√5 cm. Hence option (B) 2√(5) cm. (Trap: the area ratio is not the length ratio.)