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COMEDK20269 May 2026Morning ShiftMathematicsApplication of DerivativesActual

If 3 cm/s is the rate at which the side of an equilateral triangle increases, then the rate of change of area, when the side is 12 cm is:

Options

  1. A18 3 cm ^2 / s
  2. B18 cm ^2 / s
  3. C9 3 cm ^2 / s
  4. D6 3 cm ^2 / s

Correct answer

A. 18 3 cm ^2 / s

Step-by-step solution

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

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