Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
2x4 lumber can actually be any length; the 2 and 4 refer to width and thickness. So, you're right. –  El'endia Starman Feb 13 '12 at 23:05
Okay, thanks. Just wanted a quick check. –  Joe Feb 13 '12 at 23:12
Depends: are you meant to assume that you can subtract a total of 8 inches from the inside and 8 inches from the outside due to the thickness of the planks? –  Peter Taylor Feb 13 '12 at 23:14
Hard to know, depends on how you handle corners. Might need $2$ extra inches at each corner, actually not quite $2$ since a two by four is less than $2$ inches thick. –  André Nicolas Feb 13 '12 at 23:14
In all likelihood yours is the desired answer, if this is a textbook question. As a couple of the commenters have noted, a practical real-world answer would have to take a bit more into account. –  Brian M. Scott Feb 13 '12 at 23:24
show 1 more comment

1 Answer

up vote 3 down vote accepted

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.

share|improve this answer
Nice diagram. Makes sense - slightly quicker/easier way to the solution! –  Joe Feb 13 '12 at 23:54
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.