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Hello guys? I have been having constant disagreements with my fellow professors on this question.

A field was to be fenced using 816 posts placed 4 meters apart,leaving a 4 meter space for the gate.If 3 strands of wire were used ,what would be the total length of wire required? A.9780m C.9792m The argument is whether we add 1 to any figure with a space for a gate to get the number of items eg. trees,posts. Kindly, someone help clarify this please.

Makau Elijah
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  • The question is simply testing your understanding that there is one more post than spaces in a perimeter that starts with one post and ends with another. The answer is $A, 9780$m. $815\cdot 4\cdot 3 = 9780$ – Phil H Nov 14 '18 at 23:04
  • When you have a question like this, draw a picture with many fewer posts than $816$ and see what happens. Often that is enlightening. It should be here. – Ross Millikan Nov 14 '18 at 23:09
  • Thanks friends for clarification – Makau Elijah Nov 14 '18 at 23:32

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Consider a smaller example of a field fenced in leaving space for a gate:

$\begin{array}{ccccccc}*&-&*&&*&-&*\\|&&&&&&|\\*&&&&&&*\\|&&&&&&|\\*&-&*&-&*&-&*\end{array}$

You would notice there is one more fence post than sections of wire. This should be apparent since you can match each post with the section of wire that is clockwise around the perimeter from it for all posts with the exception of the post just before where the gate should go.

With $816$ posts we would need $815$ sections for wire, each section consisting of $3$ strands each of which $4$ meters in length.

This should give us a total of $815\cdot 3\cdot 4 = 9780$ meters of wire needed for the fence. If we decide to use some wire in constructing the gate as well then we will need to account for that as well, but as described it sounds as though the gate will be made of a different material.

JMoravitz
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