+0

# MATHCOUNTS II

+1
153
3

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
0

i got 196 but that is wrong

Nov 10, 2019
#2
+2

If needed, the diagram looks like this... Nov 10, 2019
#3
+2

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