Find the ratio of the numerical value of the area, in square units, of an equilateral triangle of side length $1$ units to the numerical value of its perimeter, in units. Express your answer as a common fraction in simplest radical form.
Area = (1/2) side^2 * sin (60°) = (1/2) * 1^2 * sqrt (3) / 2 = sqrt (3) / 4
Perimeter = 3
A / P = sqrt(3) / 4 / 3 = sqrt (3) / 12