A gardener builds a fence for a square garden that is 20 yd by 20 yd. A fence post is positioned at every corner and every 4 ft. How many fence posts will the gardener need?

Answer 1

There are multiple ways to count fence posts, but the wording of this problem practically leads you to do the easiest of them all -- draw a picture as you read and count the posts.

"A fence post is positioned at every corner" -- well, a square has 4 corners

"... and every 4 feet" -- for each of 4 sides there are 4 more fence posts:

O x x x ¤ x x x ¤ x x x ¤ x x x ¤ x x x O

That is 4 of O + 4*4 of ¤ = 20 fence posts

The interesting point about other methods (for example, going around the perimeter) is whether to count the original fence post. A square had 4 equal sides. If they are each 20 yards and posts are every 4 feet, posts at 0, 4, 8, 12, and 16 leave one needed at the end -- but with a closed figure, like a square, the original one takes care of that -- 4 sides * 5 posts is 20 fence posts.

CAUTION: Looking at the single side "drawn" above, you might be tempted to count 6 posts for each of the 4 sides.