john is going to build a rectangular plot that he needs to split into two equal areas.

The dimensions of the rectangle will be 15 feet by 112 feet.

John has sketched out the three options. Find the cost for each choice if each linear foot of fence costs $11.00 . (Example: 3 feet of fence would cost $33.0.

a is slpit horasntly
b is split verticla
and c is spit diagnoaly

1 answer

a) Splitting horizontally:

The length of the plot is 112 feet and the width is 15 feet. So, if it is split horizontally, the two equal areas would have dimensions of 56 feet by 15 feet each.

To calculate the cost, we need to find the perimeter of each area.

Perimeter of the first area = 2(56 + 15) = 142 feet
Perimeter of the second area = 2(56 + 15) = 142 feet

Total cost = (142 + 142) * 11 = 284 * 11 = $3,124

b) Splitting vertically:

The length of the plot is 112 feet and the width is 15 feet. So, if it is split vertically, the two equal areas would have dimensions of 112 feet by 7.5 feet each.

Perimeter of the first area = 2(112 + 7.5) = 239 feet
Perimeter of the second area = 2(112 + 7.5) = 239 feet

Total cost = (239 + 239) * 11 = 478 * 11 = $5,258

c) Splitting diagonally:

The length of the diagonal can be found using the Pythagorean theorem.
The length of the plot is 112 feet and the width is 15 feet.
diagonal^2 = 112^2 + 15^2
diagonal^2 = 12544 + 225
diagonal^2 = 12769
diagonal ≈ √12769
diagonal ≈ 113 feet

This means that if it is split diagonally, each area would have dimensions of approximately 112 feet by 56.5 feet.

Perimeter of the first area = 2(112 + 56.5) = 338 feet
Perimeter of the second area = 2(112 + 56.5) = 338 feet

Total cost = (338 + 338) * 11 = 676 * 11 = $7,436

Therefore, the cost for each choice is:
a) Split horizontally: $3,124
b) Split vertically: $5,258
c) Split diagonally: $7,436