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We have a garden that measures 17 feet by 20 feet. We want to pour cement for a 3-foot-wide sidewalk around the garden. To make the forms for the cement, we will need to buy some 2-by-4-inch lumber. How many feet of lumber will we need just for the perimeter of the walk? (Consider both the inside and outside perimeter.)

My solution:

I drew a picture of a garden and a sidewalk being built around the outside. The height of the inside (garden) was 17 ft and the width was 20 feet. Then, I made a 3-foot corner around all four corners of the garden. So, the height of the exterior was 17 + 3 + 3 = 23 feet, while the width was 3 + 3 + 20 = 26 feet. So, the perimeter of the inside is 74 feet and the perimeter of the outside is 98 feet. I added these two to get 172 feet as the total perimeter. Inexorably, I deemed that 172 feet of lumber was needed for the perimeter of the walk. Is that safe to assume or am I misinterpreting the question/what it is asking for? I am getting a bit "tripped up" of the fact that the problem gave me that, "to make the forms for the cement, we will need to buy some 2-by-4-inch lumber."

If anyone else cares to work out the problem/verify my solution, that would be nice.

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    Thanks for your input guys. I see there are many unaccounted for things when resembling this to a real-world problem. Alas, it is simply a textbook problem, so my answer should be sufficient - I hope.2012-02-13

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Your answer is correct: consider the following diagram.

enter image description here

So the sum of the interior and exterior perimeters of the concrete is $2 \times 17 + 2 \times 20 + 2 \times 23 + 2 \times 26 = 172 \text{ feet}.$

So long as the edging has constant width $w$ (2 inches, 4 inches, something else), this remains true; what you save on the inside, you need on the outside. So the length needed as shown in the diagram is $2 \times (17-2w) + 2 \times 20 + 2 \times 23 + 2 \times (26+2w) = 172 \text{ feet}$ again.

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    Ni$c$e diagram. Makes sense - slightly quicker/easier way to the solution!2012-02-13