John is going to build a rectangular plot that he needs to split into two equal areas. The dimensions of the rectangle will be 140 feet by 171 feet. John has sketched out three different rectangles that are split in half differently for each sketch. Find the cost for each choice if each linear foot of fence coats $10.75
Option A:?
Option B:?
Option C:?
The amount of money saved by using the cheapest option instead if the most expensive option is:?
To find the cost for each choice, we need to first calculate the perimeter of each rectangle.
For Option A: The rectangle is split along the longer side, so the dimensions of each half would be 140 feet by 85.5 feet. The perimeter of each half would then be (2 * 140 + 2 * 85.5) = 451 feet. Since we need to find the cost of fencing for both halves, multiply the perimeter by 2: 451 feet * 2 = 902 feet. Multiply this by the cost per linear foot of fence: 902 feet * $10.75/foot = $9,696.50.
For Option B: The rectangle is split along the shorter side, so the dimensions of each half would be 70 feet by 171 feet. The perimeter of each half would then be (2 * 70 + 2 * 171) = 482 feet. Since we need to find the cost of fencing for both halves, multiply the perimeter by 2: 482 feet * 2 = 964 feet. Multiply this by the cost per linear foot of fence: 964 feet * $10.75/foot = $10,377.
For Option C: In this option, the rectangle is split in the middle, resulting in two equal halves with dimensions 140 feet by 85.5 feet. The perimeter of each half would then be (2 * 140 + 2 * 85.5) = 451 feet. Since we need to find the cost of fencing for both halves, multiply the perimeter by 2: 451 feet * 2 = 902 feet. Multiply this by the cost per linear foot of fence: 902 feet * $10.75/foot = $9,696.50, which is the same as Option A.
To find the amount of money saved by using the cheapest option instead of the most expensive option, subtract the cost of the cheapest option from the cost of the most expensive option: $10,377 - $9,696.50 = $680.50. Thus, the amount of money saved is $680.50.
Bot those are wrong
I apologize for the mistake. Let's calculate the correct values.
For Option A: The rectangle is split along the longer side, so the dimensions of each half would be 140 feet by 85.5 feet. The perimeter of each half would then be (2 * 140 + 2 * 85.5) = 451 feet. Since we need to find the cost of fencing for both halves, multiply the perimeter by 2: 451 feet * 2 = 902 feet. Multiply this by the cost per linear foot of fence: 902 feet * $10.75/foot = $9,696.50.
For Option B: The rectangle is split along the shorter side, so the dimensions of each half would be 70 feet by 171 feet. The perimeter of each half would then be (2 * 70 + 2 * 171) = 482 feet. Since we need to find the cost of fencing for both halves, multiply the perimeter by 2: 482 feet * 2 = 964 feet. Multiply this by the cost per linear foot of fence: 964 feet * $10.75/foot = $10,379.
For Option C: In this option, the rectangle is split in the middle, resulting in two equal halves with dimensions 70 feet by 171 feet. The perimeter of each half would then be (2 * 70 + 2 * 171) = 482 feet. Since we need to find the cost of fencing for both halves, multiply the perimeter by 2: 482 feet * 2 = 964 feet. Multiply this by the cost per linear foot of fence: 964 feet * $10.75/foot = $10,379, which is the same as Option B.
To find the amount of money saved by using the cheapest option instead of the most expensive option, subtract the cost of the cheapest option from the cost of the most expensive option: $10,379 - $9,696.50 = $682.50. Thus, the amount of money saved is $682.50.
To find the cost for each choice, we need to calculate the perimeter of each rectangle and multiply it by the cost per linear foot of fence.
Let's first find the perimeter of the original rectangle with dimensions 140 feet by 171 feet:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (140 + 171)
Perimeter = 2 * 311
Perimeter = 622 feet
Now, let's calculate the cost for each choice:
Option A: For this option, assume the rectangle is split into two equal halves by dividing it in half along the shorter side (140 feet). So, one half will be a rectangle with dimensions 140 feet by 85.5 feet.
Perimeter of one half = 2 * (140 + 85.5)
Perimeter of one half = 2 * 225.5
Perimeter of one half = 451 feet
Total cost for option A = Perimeter of one half * Cost per linear foot
Total cost for option A = 451 feet * $10.75
Total cost for option A = $4842.25
Option B: For this option, assume the rectangle is split into two equal halves by dividing it in half along the longer side (171 feet). So, one half will be a rectangle with dimensions 85.5 feet by 171 feet.
Perimeter of one half = 2 * (85.5 + 171)
Perimeter of one half = 2 * 256.5
Perimeter of one half = 513 feet
Total cost for option B = Perimeter of one half * Cost per linear foot
Total cost for option B = 513 feet * $10.75
Total cost for option B = $5514.75
Option C: For this option, assume the rectangle is split into two equal halves by dividing it in half along the longer side (171 feet). So, one half will be a rectangle with dimensions 85.5 feet by 171 feet.
Perimeter of one half = 2 * (85.5 + 171)
Perimeter of one half = 2 * 256.5
Perimeter of one half = 513 feet
Total cost for option C = Perimeter of one half * Cost per linear foot
Total cost for option C = 513 feet * $10.75
Total cost for option C = $5514.75
To find the amount of money saved by using the cheapest option instead of the most expensive option, we subtract the cost of the cheapest option from the cost of the most expensive option:
Amount saved = Cost of most expensive option - Cost of cheapest option
Amount saved = $5514.75 - $4842.25
Amount saved = $672.50
Therefore, the cost for each choice is as follows:
Option A: $4842.25
Option B: $5514.75
Option C: $5514.75
The amount of money saved by using the cheapest option instead of the most expensive option is $672.50.