If you have 276 feet of fencing and want to enclose a rectangular area up against a long, straight wall, what?

If you have 276 feet of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Give your answer correct to the nearest square foot.|||SORRY I MISSED THE WALL ON ONE OF THE SIDES, THESE PEOPLE ARE CORRECT. I AM RIGHT IF THERE WAS NO WALL BUT A COMPLETE RECTANGULAR FENCING.


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perimeter = 276 feet = 2(l + b)


area = lb





2(l+b)=276


l+b=138


l=138-b





area = lb


a = (138-b)b


a = 138b - b虏


a' = 138 - 2b


a'' = -2





as a''%26lt;0 we have a maxima at a'=0





138-2b=0


2b=138


b=69





at b=69


l=138-b=138-69=69 feet





for b=69 feet and l=69 feet we have maximum value of area





maximum area = 69 x 69 = 4761 feet虏|||8464 sq. ft.





The biggest possible area for a rectangle is when it's a square. Take the 276 ft. of fencing and divide by 3. This equals 92 ft. So, each side of the wall is 92 ft. 92 ft. times 92 ft. equals 8464 sq. ft.|||the largest area is that approaching a square, so if each side were x themn


3x=276


x=92


92^2=8464 square feet|||A Square maximizes the are so a 92 foot square are yields 8464sq ft. You might try to vary off the square but I'm pretty sure I'm right.