SOLUTION: A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for
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-> SOLUTION: A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for
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Question 149541: A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet?
You can put this solution on YOUR website! A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet?
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Draw a rectangle representing the 18 by 13 ft garden, then draw a larger rectangle
around that one, enclosing the path around the garden.
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Label the width of the path as x
It will be apparent that the overall dimensions will be (18+2x) by (13+2x)
FOIL this to get the overall area:
(18+2x)*(13+2x) = 234 + 36x + 26x + 4x^2 = 234 + 62x + 4x^2
:
Garden area; 18 * 13 = 234
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The equation:
Overall area - garden area = path area (given as 516 sq/ft)
(4x^2 + 62x + 234) - 234 = 516
:
4x^2 + 62x - 516 = 0; our old friend, the quadratic equation
Simply divide equation by 2:
2x^2 + 31x - 258 = 0
Factor this to:
(2x + 43)(x - 6) = 0
Positive solution
x = +6 ft is the width of the path
:
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We can check this: overall dimensions will be (18+12) by (13+12)
(30*25) - 234 =
750 - 234 = 516, confirms our solution
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Did this make sense? Any questions?
