SOLUTION: Show all steps necessary to arrive at your solution. A football field is about 50 yards wide by 120 yards long. The border of uniform width around the entire field has an area o

Question 251218: Show all steps necessary to arrive at your solution.
A football field is about 50 yards wide by 120 yards long. The border of uniform width around the entire field has an area of about 1800 square yards. How wide is the border around the field?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
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.
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