$\begin{align}
& S=\frac{1}{2}a\times a\times \sin {{30}^{\circ }}\Rightarrow \frac{1}{2}\times {{a}^{2}}\times \frac{1}{2}=4\Rightarrow \frac{{{a}^{2}}}{4}=4\Rightarrow {{a}^{2}}=16\Rightarrow a=4 \\
& x=a\cos {{75}^{\circ }}+a\cos {{75}^{\circ }}=2a\cos {{75}^{\circ }}\simeq 2\times 4\times 0/3=8\times 0/3=2/4 \\
\end{align}$