Solution: Let original side be $ s $. Original area: $ \frac\sqrt34 s^2 $. New side $ s - 3 $, new area: $ \frac\sqrt34 (s - 3)^2 $. The difference: $ \frac\sqrt34 [s^2 - (s - 3)^2] = 15\sqrt3 $. Simplify: $ \frac\sqrt34 (6s - 9) = 15\sqrt3 $. Cancel $ \sqrt3 $ and solve $ \frac6s - 94 = 15 $, leading to $ 6s - 9 = 60 $, so $ s = \frac696 = 11.5 $. Original side length is $ \boxed11.5 \, \textcm $. - Nelissen Grade advocaten