Question 70083: A rectangular garden is to be surounded by a walkway of constant width. The garden's dimensions are 30 feet by 40 ft. The total area, garden pkus walkway, is to be 1800 sq. ft. What must be the width of the walkway to the nearest thousandth?
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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