Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors such that $|\overrightarrow{a}+\overrightarrow{b}|=\sqrt 3 $. If $\overrightarrow{c}=\overrightarrow{a}+2 \overrightarrow{b}+3(\overrightarrow{a} \times \overrightarrow{b})$, then $2 |\overrightarrow{c}|$ is equal to :

Question

$\begin{array}{1 1} \sqrt {55} \\ \sqrt {51} \\ \sqrt{43} \\ \sqrt{37} \end{array} $