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So I have this homework question I need help on.

There's this rectangular garden that is said dimension ($x \times y$). Someone orders said amount of cement ($c^3$) and wants to make a border of uniform width. If the border is going to be said depth ($d$), how wide should the border be?

I am given the dimensions of the garden, the amount of cement going to be used, and the depth. How would I go to tackling this problem?

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    @Srivatsan, you might consider elevating your comment to an answer.2011-09-14

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The garden has dimension $x$ by $y$. The garden with the border has dimension $x + 2w$ and $y + 2w$, where $w$ is the width you are trying to find (imagine the garden as a rectangle and the garden with a border as a larger rectangle around it). Now you are given the depth is $d$. Therefore the entire volume of the garden and border is $(x + 2w)(y + 2w)(d)$. However, only the border requires cement, so you need to subtract the volume of the garden (with depth $d$) away. Therefore, the volume of the cement is $(x + 2w)(y + 2w)(d) - xyd$. Now solve for $w$ in the following equation

$(x + 2w)(y + 2w)(d) - xyd = c$

This is a quadratic. You may need to choose the answer that makes sense.

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    @Ronnie.j: Looks fine.2011-09-15