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Question:

The angles A, B, C of a triangle ABC are in A.P. and a:b = 1:√3. If c = 4cm, then the area (in sq. cm) of this triangle is:

2√3

2√3

4√3

4√3

Solution:

∠B = π/3, by sine Rule
sinA = 1/2 ⇒ A = 30°, a = 2, b = 2√3, c = 4
Δ = 1/2 × 2√3 × 2 sq.cm = 2√3 sq.cm