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February 28th, 2012, 10:42 PM   #1
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area and perimeter

The owner of a store wants to construct a fence to enclose an outdoor storage area adjacent to the store, using all of the store as part of one side of the area. Find the dimensions that will enclose the largest area if

240 feet of fencing material are used

Can you please show me how to figure this out? How do I find area? Thank you so much for your help
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February 28th, 2012, 10:58 PM   #2
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Re: area and perimeter

The fence will make up 3 sides of the rectangle. Let x be the two sides of the rectangle made up of fencing and y be the two sides of the rectangle where one side is fence and one side is the store. x and y are measured in feet. So we have:



The area A of the fenced in area is:



Now to find the dimensions that maximize the area, we may use the axis of symmetry of the parabolic area function to do so. A parabola has the axis of symmetry:

so observing for our area function we have:

and hence:

and so .
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