2019 · Q82
The angles of a triangle are in the ratio 1:1:4. If the perimeter of the triangle is k times its largest side, then what is the value of k?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 + 2/√3
- B1 - 2/√3
- C2 + 2/√3
- D2
Explanation
Angles are 30°, 30°, 120°; sides are in ratio sin 30° : sin 30° : sin 120° = 1/2 : 1/2 : √3/2. Perimeter = (1+√3/2)t and largest side = (√3/2)t, so k = (1+√3/2)/(√3/2) = 1 + 2/√3.