Solution: The area of an equilateral triangle is $\frac{\sqrt3}4 s^2$. Solving for original side $s$: $\frac{\sqrt3}4 s^2 = 25\sqrt3 \Rightarrow s^2 = 100 \Rightarrow s = 10\,\textcm$. New side: $14\,\textcm$. New area: $\frac{\sqrt3}4 \cdot 14^2 = 49\sqrt3$. Increase: $49\sqrt3 - 25\sqrt3 = 24\sqrt3$. Thus, $\boxed{24\sqrt3}$. - Dyverse