SOLUTION: A rectangular garden is to be surrounded by a walkway of width. The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft^2. What must be th

Question 76022: A rectangular garden is to be surrounded by a walkway of width. The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft^2. What must be the width of the walkway to the earest thousandth?
The answer I came up with is 5.430 ft. Is this correct? Thanks
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 width. The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft^2. What must be the width of the walkway to the nearest thousandth?
:
5.43 does not seem right:
:
Let x = width of the walkway
:
Then the overall dimensions would be (30+2x) by (40+2x)
:
Therefore the area:
(30+2x)*(40+2x) = 1800
1200 + 140x + 4x^2 = 1800
:
Arrange as a quadratic equation
4x^2 + 140x + 1200 - 1800 = 0
4x^2 + 140x - 600 = 0
:
Simplify divide by 4:
x^2 + 35x - 150 = 0
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Use the quadratic formula: a=1; b=35; c=-150
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You should get x = +3.86 ft and obviously it's not the negative value
:
Check: 2 * 3.86 = 7.72
37.2 * 47.2 = 1799.84 ~ 1800

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