Quadratic word prob: 4x4 garden is to be surrounded with rocks evenly on 3 sides

Shadow64

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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
 
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 an approximate sketch of the situation.

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?

Continue...

If you are still stuck, please write back showing your work.
 
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
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.
 
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 think "evenly" here is translated into "path with constant width".

I would decompose it as one rectangle minus a square.
 
I think "evenly" here is translated into "path with constant width"
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.

As for the decomposition, any one of several will do.
 
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