Question

A rectangular grazing area is to be fenced off on three sides using part of a 100100 meter rock wall as the fourth side. Fence posts are to be placed every 1212 meters along the fence including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence an area 3636 m by 6060 m

Answer 1

The fewest number of posts required to fence an area of 36 meters by 60 meters is 12 posts.

How to find the least number of posts for a rectangular fence

According the information given by the statement, the number of posts ($n$) is determined by the following formula:

$n = 1 + \frac{2\cdot x_{1}+x_{2}}{d}$ (1)

Where:

• $x_{1}, x_{2}$ - Dimensions of the rectangular fence, in meters.
• $d$ - Distance between posts, in meters.

The fewest number of posts is represented by the minimum $n$ associated to a combination of $x_{1}$ and $x_{2}$.

Test 1 - $x_{1} = 36\,m$, $x_{2} = 60\,m$, $d = 12\,m$

$n = 1 + \frac{2\cdot (36\,m)+60\,m}{12\,m}$

$n = 12$

Test 2 - $x_{1} = 60\,m$, $x_{2} = 36\,m$, $d = 12\,m$

$n = 1 + \frac{2\cdot (60\,m)+36\,m}{12\,m}$

$n = 14$

Hence, the fewest number of posts required to fence an area of 36 meters by 60 meters is 12 posts. $\blacksquare$

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