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 ?
- A. 3 + \sqrt{3} units
- B. 3 + 2\sqrt{3} units ✓
- C. 3 + 3\sqrt{3} units
- D. 6 + \sqrt{3} units
Correct Answer: B. 3 + 2\sqrt{3} units
Explanation
The angles are 30^\circ, 30^\circ, and 120^\circ. The side opposite the 120^\circ angle is 3. Using the Sine Rule: a/\sin(30^\circ) = 3/\sin(120^\circ). This gives a = 3 \times (1/2) / (\sqrt{3}/2) = \sqrt{3}. Perimeter = a + a + 3 = 2\sqrt{3} + 3.