Math CentralQuandaries & Queries


Question from fee, a student:

Given a perimeter of 24cm, calculate the maximum area using quadratics.


I think you are to find the rectangle of maximum area that has perimeter 24 cm. Did you draw a diagram?

The perimeter is 24 cm so if you start at A and go half way around, say counterclockwise, to C you have gone 12 cm. Suppose the distance from A to B is x cm.

What is the distance from B to C?
What is the area of the rectangle?
Maximize this expression.


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