Question 1058725
.
You have 164 feet of fencing to enclose a rectangular region. Write an area equation in terms of width w. 
Find the dimensions of the rectangle that maximizes the enclosed area. 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


If the width is "w", then the length is {{{164/2 - w}}} = 82 - w,

and the area is A = (82-w)*w.


A rectangle having the maximal area at given perimeter is a square with the side equal to {{{1/4}}} of the perimeter.  
{{{164/4}}} = 41 feet in this case.



See the lessons 

&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>

in this site.