A) \[\sqrt{3}:(2+\sqrt{3})\]
B) \[1:6\]
C) \[1:(2+\sqrt{3})\]
D) \[2:3\]
Correct Answer: A
Solution :
\[4x+x+x=180{}^\circ \Rightarrow 6x=180{}^\circ \Rightarrow x=30{}^\circ \] \[\frac{\sin {{120}^{o}}}{a}=\frac{\sin {{30}^{o}}}{b}=\frac{\sin {{30}^{o}}}{c}\] \[\therefore a:(a+b+c)=(\sin {{120}^{o}}):(\sin {{120}^{o}}+\sin {{30}^{o}}+\sin {{30}^{o}})\] \[=\frac{\sqrt{3}}{2}:\frac{\sqrt{3}+2}{2}=\sqrt{3}:\sqrt{3}+2.\]
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