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MHT CET20249 May 2024Evening ShiftMathematicsApplication of DerivativesActual

A square plate is contracting at the uniform rate 3 ~cm ^2 / sec , then the rate at which the perimeter is decreasing, when the side of the square is 15 cm , is

Options

  1. A1 5 ~cm / sec
  2. B2 5 ~cm / sec
  3. C1 10 ~cm / sec
  4. D3 10 ~cm / sec

Correct answer

B. 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 15 3 & = 2 5 ~cm / sec aligned array l side =15 ~cm dA dt =3 ~cm ^2 / sec array

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