Question 111370
The formula for the perimeter of rectangle is {{{P=2L+2W}}}, but since we have 3 sides, the formula becomes {{{P=L+2W}}}



Now set the perimeter P equal to 80


{{{80=L+2W}}}


Now solve for L


{{{L=80-2W}}}



Now the area of a rectangle is {{{A=L*W}}}


{{{A=(80-2W)*W}}} Plug in {{{L=80-2W}}}



Now plot {{{A=(80-2W)*W}}} as a function of x. Simply change A to y and w to x to get {{{y=(80-2x)*x}}}


{{{ graph( 500, 500, -50, 50, -10, 800, (80-2x)*x) }}}


From the graph we can see that the max is at x=20, which means y=800. So when the width is 20 ft the area is maxed out at 800 square feet