SOLUTION: The length and width of a rectangle must add up to 74 feet. Calculate the dimensions that will yield the maximum area (remember, area = length times width). What is the length th

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Question 1144201: The length and width of a rectangle must add up to 74 feet.
Calculate the dimensions that will yield the maximum area (remember, area = length times width).
What is the length that results in the maximum area?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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It is a well known fact that a rectangle with a given perimeter, which has maximum area, is a square.


For the proof of this fact see the lesson

    - A rectangle with a given perimeter which has the maximal area is a square

    - A farmer planning to fence a rectangular garden to enclose the maximal area

in this site.


Based on this fact, the maximum area will be reached for a square with the side length of  74%2F2 = 37 ft.


The length and the width of this rectangle are  37 ft each.    ANSWER