Let LL' be the latus rectum through the focus of the hyperbola $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ and A' be the farther vertex. If ${\mathrm{\Delta A}}^{\mathrm{\prime }}{\mathrm{LL}}^{\mathrm{\prime }}$ is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes)

• A

  $\sqrt{3}$

• B

  $\sqrt{3}+1$

• C

  $\frac{\sqrt{3}+1}{\sqrt{2}}$

• D

  $\frac{\sqrt{3}+1}{\sqrt{3}}$