A farmer has 1 200 m wire to fence three sides of a rectangular paddock. The fourth side is a wall. Find the dimensions that will give the maximum possible area.

A farmer has 1 200 m wire to fence three sides of a rectangular paddock. The fourth side is a wall. Find the dimensions that will give the maximum possible area.

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Let width be x

length = 1 200 - 2x

Area = x(1 200 - 2x)

A = 1 200x - 2x²

$\frac{dA}{dx}$ = 1 200 - 4x

For maximum area

$\frac{dA}{dx}$ = 0

1 200 - 4x = 0

x = 300 metres

Dimensions are:

width = 300 m
length = 600 m

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johnmulu answered the question on March 7, 2017 at 07:01

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