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Twenty-four 4-inch wide square posts are evenly spaced with 5 feet between adjacent posts to enclose a square field, as shown. What is the outer perimeter, in feet, of the fence? Express your answer as a mixed number.

 Nov 10, 2019
edited by mathleteig  Nov 10, 2019
 #1
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i got 196 but that is wrong

 Nov 10, 2019
 #2
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If needed, the diagram looks like this...

 

 Nov 10, 2019
 #3
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Because there are 24 posts, and it is a square field, there are 24 / 4 = 6 posts per side.

 

Some of the sides share posts.

 

So we calculate the top and bottom sides separate from the left and right sides.

 

5 feet = 60 inches.

 

So since there are 6 posts, it is 6 * 4 = 24 inches plus, 5 * 60 = 300 inches.

 

So 24 + 300 = 324 inches.

 

324 * 2 = 648 total inches for top and bottom sides.

 

648/12 = 54 feet.

 

Because the posts are shared, we actually calculate 6 - 2 = 4 sides for each left and right side.

 

So 4 * 4 = 16 inches plus, 3 * 60 = 180 inches.

 

So 16 + 180 = 196 inches.

 

196 * 2 = 392 total inches for left and right sidses.

 

392 / 12 = \(\frac{98}{3}\) feet.

 

So the answer is \(54+\frac{98}{3}\)

 

\(86\frac{2}{3}\) feet should be the answer?

 Nov 10, 2019

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