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| Math Central | Quandaries & Queries |
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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
Thus
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.
Penny
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