Question 71278: Please help! I have no idea how to format this question nor where to start! The question is;
The plowed area of a field is a rectangle 80 feet by 120 feet. The owner plans to plow an extra strip of uniform width on each of the four sides of the field, in order to double the plowed area. How many feet should he add to each dimension? (draw a diagram first)
Thanks for your time!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The plowed area of a field is a rectangle 80 feet by 120 feet. The owner plans to plow an extra strip of uniform width on each of the four sides of the field, in order to double the plowed area. How many feet should he add to each dimension? (draw a diagram first)
:
First find the area of the original field: 80 * 120 = 9600 sq ft
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The area after the strip has been plowed: 2 * 9600 = 19200 sq ft
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Let the uniform width of the extra plowed area = x
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Dimensions of the new field:
(80 + 2x) by (120 + 2x)
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then: (80+2x)*(120+2x) = 19200 sq ft
FOIL
9600 + 160x + 240x + 4x^2 = 19200
9600 + 400x + 4x^2 - 19200 = 0
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A quadratic equation:
4x^2 + 400x - 9600 = 0
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Simplify divide equation by 4
x^2 + 100x - 2400 = 0
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Factors to:
(x + 120)(x - 20)
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x = +20 ft is solution we want, the width of the added plowed area
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40 feet is added to both dimensions:
New dimensions would be 160 by 120
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Check solution using area: 160 * 120 = 19200 sq ft
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