A fence of length 100m is to be used to form three sides of a rectangular enclosure, the fourth side being a wall then the maximum

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1. Given : A fence of length 100m is to be used to form three sides of a rectangular enclosure,

   the fourth side being a wall

   To Find : the maximum area which can be enclosed by the fence is

   Solution:

   Let say side opposite to wall = 2x m

   Then sum of remaining two sides = 100 – 2x m

   Length one of remaining side = (100 – 2x)/2 = 50 – x m

   Area = (50 – x) (2x)

   =>A = 100x – 2x²

   dA/dx = 100 – 4x

   dA/dx = 0

   => 100 – 4x = 0

   => x = 25

   d²A/dx² = – 4 < 0

   Hence area is maximum when x = 25

   Hence Area = (50 – x) (2x)

   => Area = (50 – 25) (2 * 25)

   => area = 25 * 50

   => area = 1250 m²

   maximum area which can be enclosed by the fence is 1250 m²

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