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Question 1195250: Eight meters of fencing are available to enclose a rectangular play area.
A. What is the maximum area that can be enclosed?
B. What dimensions produce the maximum area?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Eight meters of fencing are available to enclose a rectangular play area.
A. What is the maximum area that can be enclosed?
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2 meters sides ---> 4 sq meters
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B. What dimensions produce the maximum area?
2 by 2 meters
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
At given perimeter, a rectangle having maximum area is a square with the side length
equal to one fourth (1/4) of the given perimeter.
It is a classic problem on finding optimal dimensions.
This problem was solved MANY TIMES in this forum.
Therefore, I created lessons at this site, explaining the solution in all details.
The lessons are under these links
- 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
Read these lessons attentively.
Consider them as your TEMPLATE.
Having these templates in front of you, solve the GIVEN problem by the same way.
Having it written once as a lesson in compact and clear form,
I do not see any reasons to re-write it again and again with each new given input data set.
By the way, in these lessons, you will find many useful links to accompanied lessons.
Do not miss them.
Consider my lessons as your textbook, handbook, tutorial and (free of charge) home teacher.
In your case, the maximum fenced area is 4 m^2, provided by a square with the side length of 8/4 = 2 meters.
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