Question 885168: A rectangular field with dimensions of 30 meters by 50 meters is to be surrounded by a fence. Posts are placed every 2 meters. a)How many posts are needed.
b)How many posts are needed if one 50 meter side is not fenced? c)How many posts are needed if one 30 meter side is not fenced?
So I did fine on the first part--I got 80 posts, but then for part b and c I got 55 and 65, but the answer in the back says 56 and 66. I don't understand why it is one more!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! a) The perimeter of that field (in meters) is
 .
That is  2-meter stretches of fencing.
Each 2-meter stretch of fence starts at 1 post,
and counting the starting posts is all we need,
because the post at the end of each 2-meter stretch
is already counted as the starting post of the next 2-meter piece of fence.
So  posts are needed.
b) If one of the 50-meter sides does not need to be fenced,
the length of fence you need (in meters) is
 .
That will be  2-meter pieces of fence.
You start at one corner of the side that does not need fence,
and start installing fence on the 30-meter side that starts from that corner.
You put one post at that corner: the starting post of the first 2-meter stretch of fence,
and you keep adding one more post and one more section of fence, all around the 3 sides that need fence.
When you have installed 55 starting posts and 55 pieces of fence,
you need one more post at the end of fence section number 55.
That post is not the starting post of the next section of fence,
because there is no next section of fence.
So you need  posts.
c) It is just like part b).
You need a starting post for each of the 2-meter section of fence,
and you also need an ending post for the last 2-meter section of fence.
You need  meters of fence.
That is  2-meter sections of fence.
That means  starting posts, one for each of the 65 sections of fence,
and  more post at the end of the last section.
That is  posts.
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