CAT 2022 Slot 2 QA · Question 21

The length of each side of an equilateral triangle $\mathrm{ABC}$ is $3\mathrm{cm}$. Let $\mathrm{D}$ be a point on $\mathrm{BC}$ such that the area of triangle $\mathrm{ADC}$ is half the area of triangle $\mathrm{ABD}$. Then the length of $\mathrm{AD}$, in $\mathrm{cm}$, is