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Question: In a\(\triangle A B C\) if \(a = 2 x , b = 2 y\) and \(\angle C = 120 ^ { \circ }\), then the area o...

In a△ABC\triangle A B C if a=2x,b=2ya = 2 x , b = 2 y and ∠C=120∘\angle C = 120 ^ { \circ }, then the area of the triangle is

A

xy

B

xy3x y \sqrt { 3 }

C

3xy3 x y

D

2xy2 x y

Answer

xy3x y \sqrt { 3 }

Explanation

Solution

Δ=12absin⁡C=12⋅2x⋅2ysin⁡120∘=3xy\Delta = \frac { 1 } { 2 } a b \sin C = \frac { 1 } { 2 } \cdot 2 x \cdot 2 y \sin 120 ^ { \circ } = \sqrt { 3 } x y .