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