Point $P$ is inside equilateral $△ABC$. Points $Q$, $R$, and $S$ are the feet of the perpendiculars from $P$ to $\overline{AB}$, $\overline{BC}$, and $\overline{CA}$, respectively. Given that $PQ=2$, $PR=3$, and $PS=4$, what is $AB$?