Math CentralQuandaries & Queries


Question from rachel, a student:

A rectangular field is to be enclosed by 400m of fence. What dimensions will give a maximum area?

Hi Rachel,

Suppose the field is L metres lang and W metres wide. The length of fencing is then 2L + 2W meters. Hence

2L + 2W = 400 metres

and the area is given by

Area = L × W square metres.

Solve the first equation for W and substitute the value you obtain into the second equation. This will result in the area being expressed as a quadratic function in the variable L. Use what you know about quadratic functions to find the value of L that maximizes this expression.

I hope this helps,

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