Question 29
A point $O$ is inside an equilateral triangle $PQR$ and the perpendiculars $OL,OM$ and $ON$ are drawn to the sides $PQ,QR$ and $RP$ respectively. The ratios of lengths of the perpendiculars $OL:OM:ON$ is $1:2:3$. If $\dfrac{\text{area of }LONP}{\text{area of }\triangle PQR}=\dfrac ab$, where $a$ and $b$ are integers with no common factors, what is the value of $a+b$?
