SOLUTION: Beginning witha fixed length of fence, a free-standing rectangular enclosure is built so that it encircles the maximum area. Show that this enclosure is actually a square. Remember

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Question 118356: Beginning witha fixed length of fence, a free-standing rectangular enclosure is built so that it encircles the maximum area. Show that this enclosure is actually a square. Remember that all squares are rectangles.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let 2k="length of fence", y="length of enclosure", x="width of enclosure"

perimeter=2x+2y ___ 2k=2x+2y ___ k=x+y ___ k-y=x

area=x*y ___ a=(k-y)y ___ a=ky-y^2

the maximum area is at the axis of symmetry ___ y=-k/(2(-1)) ___ y=k/2

x+y=k ___ x+(k/2)=k ___ x=k/2

x=y ___ width=length ___ definition of square