Question 1205762
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Find the dimension of a rectangle that will yield the maximum area 
{{{highlight(cross(of))}}} <U>if</U> its perimeter is 54 meters. What is the maximum area? 
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At given perimeter, a rectangle having maximum area is a square with the side length 

equal to one fourth &nbsp;(1/4) &nbsp;of the given perimeter.



It is a classic problem on finding optimal dimensions.


This problem was solved &nbsp;MANY &nbsp;TIMES &nbsp;in this forum.


Therefore, &nbsp;I created lessons at this site, &nbsp;explaining the Algebra solution in all details.


The lessons are under these links

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-rectangle-with-the-given-perimeter-which-has-the-maximal-area-is-a-square.lesson>A rectangle with a given perimeter which has the maximal area is a square</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-farmer-planning-to-fence-a-rectangular-garden-to-enclose-the-maximal-area.lesson>A farmer planning to fence a rectangular garden to enclose the maximal area</A>


Read these lessons attentively.

Consider them as your &nbsp;TEMPLATE.


By the way, &nbsp;in these lessons, &nbsp;you will find many useful links to accompanied lessons.

Do not miss them.


Consider my lessons as your textbook, &nbsp;handbook, &nbsp;tutorial and &nbsp;(free of charge) &nbsp;home teacher.



In your case, &nbsp;the maximum area is provided by a square with the side length of &nbsp;{{{54/4}}} = 13{{{1/2}}} = 13.5 meters.


The maximum area in this case is  &nbsp;&nbsp;13.5*13.5 = 182.25 square meters.