Question 242059: I need help with this problem. Fencing a garden. Elka is planning a rectangular garden that is to be twice as long as it is wide. If she can afford to buy at most 180 feet of fencing, then what are the possible values for the width?
Answer by College Student(505)   (Show Source):
You can put this solution on YOUR website! There are three possible solutions, but I'm only going to work two of them. You may do the third one if you see fit.
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Possibility 1: If the rectangular garden is away from any structure, the 180 feet of fencing will be distributed among 4 sides.
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Possibility 2: If the rectangular garden is located next to a structure (a house, garage, a shed, a neighbor's fence, etc.), where only three sides of fencing are needed, then the width would be larger.
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Possibility 3: If the rectangular garden is cornered by two structures where only two sides of fencing are needed, then the width would be at its largest.
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The problem tells us the fence will be 180 feet long. It also says the lenght is twice as much as its width. If we let: p = perimeter, x = width, and 2x = lenght, our equation then becomes:  I have multiplied x and 2x by 2 because there are two sides for width and two for lenght.
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 <--- this is the width of one side IF the rectangular garden is fenced on all four sides.
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Now, if the rectangular garden is fenced on only three sides, here's how the equation would look like:  ... two widths, but only one lenght.
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 <--- this is the width of one side IF the rectangular garden is fenced only on three sides. The other being covered by a structure.
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If the rectangular garden is fenced on only two sides, here's how the equation would look like:  ... one width and one lenght. I'll let you work out the third possibility by using this equation.
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The answer to the problem is most likely the first one I showed you, but you might impress your professor when you present all possibilities.
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Now, the same can not be said if the garden was enclosed by three structures because then we would not have a width and a length, just straight fencing. It would definitely not work for this problem.
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Hope this helped!
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