Question 160

A farmer has decided to build a wire fence along one straight side of this property. For this, he planned to place several fence-posts at six metre intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was five less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them eight metres apart. What is the length of the side of his property and how many posts did he buy?

Solution

Let the number of posts the farmer bought = x
Length of the side = (x+5-1)*6 = 6*(x+4)
Length of the side is also equal to (x-1)*8
=> 8x - 8 = 6x + 24 => x = 16
Length of side = 6*20 = 120 m

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