Q. 355.0( 1 Vote )

# 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 cm^{2}/s

B. cm^{2}/s

C. cm^{2}/s

D. cm^{2}/s

Answer :

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 cm^{2}/s.

So the correct option is option C.

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The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate if its area increasing when the side of the triangle is 20 cm?

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