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JEE Main2012MathematicsApplication of DerivativesActual

Consider a rectangle whose length is increasing at the uniform rate of 2 ~m / sec , breadth is decreasing at the uniform rate of 3 ~m / sec and the area is decreasing at the uniform rate of 5 ~m ^2 / sec . If after some time the breadth of the rectangle is 2 ~m then the length of the rectangle is

Options

  1. A2 ~m
  2. B4 ~m
  3. C1 ~m
  4. D3 ~m

Correct answer

D. 3 ~m

Step-by-step solution

Let A be the area, b be the breadth and be the length of the rectangle. Given: d A d t =-5, d d t =2, d b d t =-3 We know, A= b aligned & d A d t = d b d t +b d d t =-3 +2 b & -5=-3 +2 b . aligned When b=2 , we have -5=-3 +4 = 9 3 =3 m

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