The length of each side of an equilateral triangle $\mathrm{A B C}$ is $3 \mathrm{~cm}$. Let $\mathrm{D}$ be a point on $\mathrm{B C}$ such that the area of triangle $\mathrm{A D C}$ is half the area of triangle $\mathrm{A B D}$. Then the length of $\mathrm{A D}$, in $\mathrm{cm}$, is
- $\sqrt{7}$
- $\sqrt{6}$
- $\sqrt{8}$
- $\sqrt{5}$