# How many posts are needed to surround the perimeter? [closed]

Julie's garden with perimeter of 54 ft and width of 12 ft is to have posts put around it 3 feet away from the garden's edge on all sides. They are also to be three feet apart. how many posts will she need?

• I think it does work, but this doesn’t really remind me of a puzzle so much as it does a word problem from a set of math homework. I might vote to close this because of that; and if closed I will remove my answer. Sep 8, 2018 at 12:40
• I agree with @El-Guest as this is just a normal math homework that I used to get from school. Voting to close this :D Sep 8, 2018 at 13:00

Julie’s garden

Will be $15 \times 12$ yielding a $54$ foot perimeter. If we add 3 feet to all sides, we have a length of $21$ feet and a width of $18$ feet. This means we’ll need 8 posts for the length and 7 posts for the width; and then we need to deduct 4 posts since we counted the corners twice.

$8+8+7+7-4 = 26$ posts.
The resulting fence shape looks like a running track, albeit more square than that. We must compute the total perimeter. We see that the shape has to have straightaway stretches of 15 feet and 12 feet for the lengths and widths respectively. At each corner, we create a quarter circle of radius 3 away from the corner. The total perimeter of this shape is therefore $54 + 6\pi$ feet. Spacing each post 3 feet apart would therefore require $18 + 2\pi \approx 24$ posts, although each post wouldn’t be exactly 3 feet apart from each other.
• You’d have to do some shifting around the corners though, because taking out the corner post leaves the two posts nearest the corner $3\sqrt{2}$ feet apart I believe. Sep 8, 2018 at 14:05