Math CentralQuandaries & Queries


Question from Julirose, a student:

The perimeter of a rectangle is 38 meters. Find the dimensions of the rectangle that will contain the greatest area.

Hi Julirose,

Let the length of the rectangle be L metres and the width be W metres.


Since the perimeter is 38 metres

L + W = 38/2 = 19 metres


L = 19 - W

The area A of the rectangle is given by

A = L ×W

Use the first equation to write the area as a function of one variable W and then use calculus or your knowledge of parabolas to maximize the area.


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