2015 · Q52
The angles of a triangle are in the ratio 4:1:1. Then the ratio of the largest side to the perimeter is
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2/3
- B1/(2 + √3)
- C√3/(2 + √3)
- D2/(1 + √3)
Explanation
Angles 120°, 30°, 30°: largest side = 2R·sin120° = R√3; perimeter = 2R(sin120° + 2sin30°) = R(√3+2). Ratio = √3/(2+√3) (option C).