You need to make a goat pen in SHSID farm, you have some 3 foot sections of fence, how many sections of fence is needed for rectangular goat pen that is 12 ft x 24ft? If you want as much space as possible with no more fence material, how to rearrange the length and width? (You may not cut the fence section.)

Question

You need to make a goat pen in SHSID farm, you have some 3 foot sections of fence, how many sections of fence is needed for rectangular goat pen that is 12 ft x 24ft? If you want as much space as possible with no more fence material, how to rearrange the length and width? (You may not cut the fence section.)

Answer 1

To find the number of fence sections needed for a 12ft x 24ft rectangular goat pen, we need to calculate the perimeter of the pen.

Perimeter = 2(length) + 2(width)
Perimeter = 2(12ft) + 2(24ft)
Perimeter = 24ft + 48ft
Perimeter = 72ft

Each section of fence is 3ft long, so we need 72ft / 3ft = 24 sections of fence for the rectangular goat pen.

To rearrange the length and width for the goat pen to use as much space as possible with no more fence material, we should aim for a square pen. The dimensions would have to be the maximum possible while keeping the perimeter at 72ft.

For a square pen, the length would be equal to the width. Let L be the length and W be the width.

Perimeter = 2(L) + 2(W) = 72ft
2(L+W) = 72ft
L+W = 36ft

Since we want the pen to be a square, L = W. Therefore,
2L = 36ft
L = 18ft

So, the dimensions of the new square goat pen would be 18ft x 18ft. This arrangement would use as much space as possible with the given fence material.