Question 251218
This can be solved by considering the football field as the amount to be subtracted from the area of the larger rectangle defined by the border.
A = L * W for all rectangles, where A = area, L = length, and w = width.
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We are told the field is 50 x 120 = 6000.
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The area of the rectangle defined by the outside border is 7800, that is, 1800 more than the field.
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The unknown width of the border will be called 'x'.
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Along the lengths:  120*x + 120*x for both sides.
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Along the widths:  50*x + 50*x for both ends.
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AND there are 4 corners, each of which will be x*x in area.
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Combining what we know:
4x^2 + 340x = 1800
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Divide both sides by 4
x^2 + 85x = 450
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Subtracting 450 from both sides
x^2 + 85x - 450 = 0
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Can we factor 450 such that we can define +85x and -450?
Yes, 5 * 90 = 450 and 90-5=85.
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(x+90)(x-5)= 0
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So we have two candidate answers for the width:  x=-90 and x=5.
A negative value is nonsensical, so we estimate the border is 5 yards wide.
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Done.