## 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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Mathematics
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2021-07-19T22:19:56+00:00
2021-07-19T22:19:56+00:00 1 Answers
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## 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 isSolution: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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