The angles A, B and C of a triangle are in the ratio 1 : 1 : 4. If the longest side of the triangle is 3 units, then what is the perimeter of the triangle?

Angles are 30°, 30°, 120°. Side opposite 120° is longest = 3. By sine rule: a/sin 30° = 3/sin 120°, so a = 3 · (1/2)/(√3/2) = 3/√3 = √3. Two sides are √3 each, longest is 3. Perimeter = 3 + 2√3. Wait: that gives option (b). Let me recheck: a/sin A = 3/sin 120°. a = 3 sin 30°/sin 120° = 3(1/2)/(√3/2) = 3/√3 = √3. So two sides √3 and one side 3. Perimeter = 3 + 2√3, which is option (b).