In $\triangle{LEO}$, point $J$ lies on $\overline{LO}$ such that $\overline{JE}\perp\overline{EO}$, and point $S$ lies on $\overline{LE}$ such that $\overline{JS}\perp\overline{LE}$. Given that $JS=9, EO=20,$ and $JO+SE=37$, compute the perimeter of $\triangle{LEO}$.