Question 69884: A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30ft by 40ft. The total are, garden plus walkway, is to be 1800ft^2. What must be the width of the walkway to the nearest thousandth?
Thank you for helping, these problems confuse me all the time!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30ft by 40ft. The total area, garden plus walkway, is to be 1800 ft^2. What must be the width of the walkway to the nearest thousandth?
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A rough drawing will aid in understanding this:
Label the garden rectangle as 30 by 40
Label the width of the walk-way as x,
It should be apparent, that the outside dimensions, which include the walk-way,
are (30+2x) by (40+2x):
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Area of the whole thing is given as 1800 sq ft, so we have:
(30+2x)*(40+2x) = 1800
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1200 + 60x + 80x + 4x^2 = 1800; FOILed (30+2x)(40+2x)
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1200 + 140x + 4x^2 - 1800 = 0;
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4x^2 + 140x - 600 = 0; our old friend, the quadratic equation
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Simplify, divide equation by 4 and you have:
x^2 + 35x - 150 = 0
Does not easily factor, so use the quadratic formula:
a = 1; b = 35; c = -150
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We are only interested in the positive solution here
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x = 3.860 ft is the width of the path
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Check our solution; add 2 * 3.86 to the given dimensions; 30 by 40
37.72 * 47.72 = 1799.9984 ~ 1800
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How about this? Did it make sense to you?
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