Let the side of the equilateral triangle be x cm, then the area of the equilateral triangle is

So as per the question rate of side increasing at instant of time t is dx/dt = 2 cm/sec

Now differentiating area with respect to time t, we get

Now substituting the given value of dx/dt, we get

Hence, the rate at which the area increases, when side is 10 cm is 10√3 cm^{2}/s.

**So the correct option is option C.**