Question 242059
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: {{{p=2(x)+2(2x)}}}  I have multiplied x and 2x by 2 because there are two sides for width and two for lenght.
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{{{p=2(x)+2(2x)}}}
{{{180= 2x+4x}}}
{{{180=6x}}}
{{{180/6=x}}}
{{{x=30}}} <--- 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:  {{{p=2(x)+1(2x)}}} ... two widths, but only one lenght.
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{{{p=2(x)+1(2x)}}}
{{{180=2x+2x}}}
{{{180=4x}}}
{{{180/4=x}}}
{{{x=45}}} <--- 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:  {{{p=x+2x}}} ... 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!