# If each side of an equilateral triangle increases at the rate of √2 cm/sec, find the rate of increase of its area

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If each side of an equilateral triangle increases at the rate of √2 cm/sec, find the rate of increase of its area when its side of length is 3 cm.

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If x cm is the side of the equilateral triangle and A is its area, then A = √3/4 x2

Differentiating w.r.t. f, we get

Hence, rate of increase of the area of equilateral triangle = 3√6/2 cm2/sec.