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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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    First let the unknown border width be $w$. Calculate the area of the border in terms of $w$. To do this, you will need to split up the border into some rectangles whose dimensions you know, and then add all the areas up. Second step: if this area is $A$ and the depth is $d$, then how much cement would you need?2011-09-14
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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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    Thanks! this allowed me to both answer the question and undestand how to do it2011-09-14
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    A nit: the cement volume was specified as $c^3$2011-09-14
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    yea im having difficulty again :/. lets say for instance, the measurement are in meters (which they are not). the garden is 3*5 meters and some person orders one decameter^3 amount of cement. And the depth is 4 cm. I don't know if these numbers would match or not, but how would I use your formula? (note:my givens are in different units in my question)2011-09-14
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    and by decameter^3 i mean like decameter cubed2011-09-14
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    Convert everything into the same unit. For example, 4 cm is .04 m. Decameter is 10 meters right? If this is the case, note that 1 decameter cubed is 10^3 meter cubed2011-09-14
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    You'd need to match the units. If you use a measurement in meters, then all other measurements have to be in meters.2011-09-14
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    Ok let me tell you the units and what i am doing...the rectangle is 6*10 ft, the cement is 1 cubic yard, and the depth is 3 inches...tell me if i used the formula correctly...(6ft*2w)(10ft*2w)(.25ft)-(6ft*10ft*.25ft)=27 feet cubed2011-09-14
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    It should by $(6 + 2w)(10 + 2w)(.25) - (6)(10)(.25) = 27$. I am not sure what the * mean.2011-09-14
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    ook. i got up to (8ft^2)*w+1ft(w^2)=27ft^3...i am stuck as to what to do next2011-09-14
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    i got sqrt(43)-4...i think i messed up2011-09-14
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    @Ronnie.j: Looks fine.2011-09-15