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 area which can be enclosed by the fence is_________________
Answers
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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