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?
closed as off-topic by El-Guest, JonMark Perry, Bass, Glorfindel, Quintec Sep 8 '18 at 23:06
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – El-Guest, JonMark Perry, Bass, Glorfindel, Quintec
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.
The answer is therefore
$8+8+7+7-4 = 26$ posts.
@Jaap Scherphuis has raised an excellent extension in the comments below. We ought to round the corners such that we minimize the perimeter.
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.