A rectangular yard 75 feet by 135 feet has a fence with a post every five feet.How many posts are needed for the entire fence?
perimeter = 2(75+135) = 420
number of 4 ft lengths = 420/5 = 84
so we need 84 posts
(look at the first length of 75 feet. Let's put a post at the end of each 5 ft stretch, that would take take 15 posts. Notice that the beginning of that side still has no post, but the beginning of the 135 ft side already has a post, so for this side in the same way we need 27 post, another 15 for the next side and finally 27 for the last side.
Notice that the last post filled in our missing starting point)
To determine the number of posts needed for the entire fence, we need to calculate the perimeter of the rectangular yard and then divide it by the distance between each post.
First, let's calculate the perimeter of the yard. The formula to find the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
The length of the yard is 75 feet and the width is 135 feet, so the perimeter would be:
Perimeter = 2 * (75 + 135) = 2 * 210 = 420 feet
Now, dividing the perimeter by the distance between each post, which is 5 feet, will give us the total number of posts needed:
Number of posts = Perimeter / Distance between posts
Number of posts = 420 / 5 = 84
Therefore, you will need a total of 84 posts for the entire fence.