QJEEM19Mad9ff: JEE Main 2019 Mathematics - Class 11 JEEM19Mad9ff Solution: The angles A, B and C of a triangle ABC are in A.P. and a : b = …

Question

Verified Solution • 2025–26 Session moderate

The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 :

\sqrt{3}

. If c = 4 cm, then the area (in sq. cm) of this triangle is :

Accepted Answer

From the question 2B = A + C & A + B + C =

π

\Rightarrow

3B =

π

\Rightarrow

B =

\frac{π}{3}

∴ A + C = \frac{2 π}{3} σ

\frac{a}{b} = \frac{1}{\sqrt{3}}

\frac{2 R \sin A}{2 R \sin B} = \frac{1}{\sqrt{3}}

sin A =

\frac{1}{2}

∴

A = 30^o

∴

a = 2, b = 2

\sqrt{3}

, c = 4

Δ = \frac{1}{2} \times 2 \sqrt{3} \times 2 = 2 \sqrt{3}

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