USAMO 1982 Problem 3

$\mathrm{D}$ is a point inside the equilateral triangle $\mathrm{ABC}$. $\mathrm{E}$ is a point inside $\mathrm{DBC}$. Show that area $\mathrm{DBC} /($ perimeter $\mathrm{DBC})^{2}>$ area $\mathrm{EBC} /(\text { perimeter } \mathrm{EBC})^{2}$.