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Quadratic word prob: 4x4 garden is to be surrounded with rocks evenly on 3 sides
- Thread starter Shadow64
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D
Deleted member 4993
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First draw an approximate sketch of the situation.There is a 4x4 garden that is to be surrounded with rocks evenly on three sides. The area covered by the rocks is equal to the area of the garden. What is the width of soil to be filled in with rocks?
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Let the width of the rock-path = W
Then
What is the total area of the rectangle (garden + path)?
What is the area of the rock-path?
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If you are still stuck, please write back showing your work.
This is a hard problem for two reasons. First, "evenly" is not a perfectly clear description. Second, even if you draw a diagram, AS YOU SHOULD, the real work will be to figure out how to decompose the diagram into a useful form. I can see at least three ways to do that. Each will lead to a different equation, all of which will lead to the same answer.There is a 4x4 garden that is to be surrounded with rocks evenly on three sides. The area covered by the rocks is equal to the area of the garden. What is the width of soil to be filled in with rocks?
Please show all steps
First draw the diagram. I suspect that the most intuitive way to decompose the border is into three rectangles and two squares.
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Deleted member 4993
Guest
I think "evenly" here is translated into "path with constant width".This is a hard problem for two reasons. First, "evenly" is not a perfectly clear description. Second, even if you draw a diagram, AS YOU SHOULD, the real work will be to figure out how to decompose the diagram into a useful form. I can see at least three ways to do that. Each will lead to a different equation, all of which will lead to the same answer.
First draw the diagram. I suspect that the most intuitive way to decompose the border is into three rectangles and two squares.
I would decompose it as one rectangle minus a square.
I suspect that was the intended meaning as well, but there are different interpretations possible, such as constant minimum distance. You can never tell whether the original problem or the student's paraphrase was ambiguously stated.I think "evenly" here is translated into "path with constant width"
As for the decomposition, any one of several will do.