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Determine maximum enclosed area

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Determine maximum enclosed area

A farmer has 100 metres of fencing wire from which to build a rectangular chicken-run. He intends using two adjacent walls for two sides of the rectangular enclosure.

asked Feb 24, 2021 by anonymous

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1 Answer

If one fenced side is length x, the other fenced side will be 100-x.

The area A=x(100-x)=100x-x².

A=100x-x²,

A=2500-2500+100x-x²,

A=2500-(2500-100x+x²),

A=2500-(50-x)².

This has a maximum value when x=50m and the area is 2500m².

So the area is square with side 50m.

answered Feb 24, 2021 by Rod Top Rated User (1.2m points)

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