## 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

Question

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_________________​

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3 months 2021-07-19T22:19:56+00:00 1 Answers 0 views 0

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