Question 17
Point $P$ is inside equilateral $\triangle ABC.$ Points $Q,$ $R,$ and $S$ are the feet of the perpendiculars from $P$ to $\overline{AB},$ $\overline{BC},$ and $\overline{CA},$ respectively. Given that $PQ = 1,$ $PR = 2,$ and $PS = 3,$ what is $AB?$