If 2 : ( 1 + 3 ) :: 6 : x , then x is equal to -

Answer: Option A

$$\begin{array}{rl}& =\sqrt{2}:\left(1+\sqrt{3}\right)::\sqrt{6}:x\\ & \Rightarrow \sqrt{2}x=\sqrt{6}\left(1+\sqrt{3}\right)\\ & \Rightarrow x=\frac{\sqrt{6}\left(1+\sqrt{3}\right)}{\sqrt{2}}\\ & =\sqrt{3}\left(1+\sqrt{3}\right)\\ & =\sqrt{3}+3\end{array}$$