Question 495698
Area of a rectangle = Length * Width
{{{A = area}}}
{{{A = 120}}}  (given)
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{{{L = length}}}
{{{W = width}}}
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Length is 8 ft greater than twice the width. (given)
{{{L = 2W + 8
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What are the length and width?
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{{{L*W = A}}}
{{{L*W = 120}}}
Substitute for L 
{{{(2W+8)*W = 120}}}
Multiply
{{{2W^2 + 8W = 120}}}
Subtract 120 from both sides
{{{2W^2 + 8W - 120 = 0}}}
Divide by 2 to eliminate the coefficient on W^2
{{{W^2 + 4W - 60 = 0}}}
Factor
{{{(W +10)(W -6) = 0}}}
So the width is either -10 or 6.
A negative width is nonsense, so we decide:
{{{W = 6}}}
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Substitute for W
{{{L*6 = 120}}}
Divide both sides by 6
{{{L = 20}}}
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ALWAYS check your work.
In this case, you cannot use the area to check because you used it to solve for L.
Looking back you can find:
{{{L = 2W + 8}}}
{{{2W + 8 = 2(6) + 8}}}
{{{2W + 8 = 20}}}
Correct.
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Answer:
Length = 20 ft.
Width = 6 ft.
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Done