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MHT CET202310 May 2023Morning ShiftMathematicsApplication of DerivativesActual

A square plate is contracting at the uniform rate 4 ~cm ^2 / sec , then the rate at which the perimeter is decreasing, when side of the square is 20 ~cm , is

Options

  1. A1 5 ~cm / sec .
  2. B4 ~cm / sec .
  3. C2 ~cm / sec .
  4. D2 5 ~cm / sec .

Correct answer

D. 2 5 ~cm / sec .

Step-by-step solution

Let A , P and X be the area, perimeter and length of side of square respectively at time ' t ' seconds. Then, aligned A & = X ^2, P =4 X P & =4 A aligned Differentiating w.r.t. t, we get aligned dP dt & =4 1 2 A dA dt & = 2 X dA dt & = 2 20 4... [ array l side =20 ~cm dA dt =4 ~cm ^2 / sec array ] & = 2 5 ~cm / sec aligned

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