The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when side is 10 cm is:

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

Now differentiating area with respect to time t, we get

Taking out the constants we get,

Now applying the derivative, we get

Now substituting the given value of , we get

So when side x=10cm, the above equation becomes,

Hence, the rate at which the area increases, when side is 10 cm is 10√3 cm²/s.

So the correct option is option C.