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Question 1184978: mang jose wants to enclose his rectangular garden with 120 meters of fencing materials. what are the dimensions of the rectangle that will maximize the enclosed area.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source):
Answer by ikleyn(52803)  (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 (and many times as solved problems in response to the visitors requests),
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 area is provided by a square with the side length of 120/4 = 30 meters.
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