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MHT CET202618 April 2026Morning ShiftMathematicsApplication of DerivativesActual

If the side of an equilateral triangle increases at the rate of 3 cm/sec , then the rate of change of increase of its area when the side is 12 cm is ____

Options

  1. A18 cm ^2/ sec
  2. B10 cm ^2/ sec
  3. C12 cm ^2/ sec
  4. D3 3 cm ^2/ sec

Correct answer

A. 18 cm ^2/ sec

Step-by-step solution

Let the side of the equilateral triangle be a and its area be A . Given da dt = 3 cm/sec and a = 12 cm . The area of an equilateral triangle is given by A = 3 4 a^2 . Differentiating with respect to time t : dA dt = 3 4 2a da dt dA dt = 3 2 a da dt Substituting the given values: dA dt = 3 2 12 3 dA dt = 6 3 = 18 cm ^2/ sec Answer: 18 cm ^2/ sec

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