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MHT CET202014 Oct 2020Morning ShiftMathematicsApplication of DerivativesActual

A metal wire 108 meters long is bent to form a rectangle. If the area of the rectangle is maximum, then its dimensions are

Options

  1. A28 ~m , 28 ~m
  2. B27 m, 27 ~m
  3. C25 ~m , 25 ~m
  4. D26 ~m , 26 ~m

Correct answer

B. 27 m, 27 ~m

Step-by-step solution

Let sides of rectangle be x and y Thus 2 x+2 y=108 x+y=54 y=54-x Now Area =A=x y =x(54-x)=54 x-x² Differentiating w.r.t. x , we get d A dx =54 1-2 x and d ² ~A dx ² =-2 < 0 When d A d x =0 , we get 54-2 x=0 x=27 y=54-x=27

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