# 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:

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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:

A. 10 cm2/s
B. √3 cm2/s
C. 10√3 cm2/s
D. 10/3 cm2/s

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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 cm2/s.

So the correct option is option C.