To find the cost of each choice, we need to calculate the length of the fence required for each option and multiply it by the cost per linear foot.
Option A: We need to divide the rectangle into two equal areas using a horizontal line. This means we have two rectangles, each with dimensions 95 feet by 84 feet (half the original dimensions).
The length of the fence required for each rectangle is:
95 + 84 + 95 + 84 = 358 feet (2 sides of length 95 and 2 sides of length 84).
The cost for Option A = 358 * $10.75 = $3,850.5.
Option B: We need to divide the rectangle into two equal areas using a vertical line. This means we have two rectangles, each with dimensions 47.5 feet by 168 feet (half the original dimensions).
The length of the fence required for each rectangle is:
47.5 + 168 + 47.5 + 168 = 431 feet (2 sides of length 47.5 and 2 sides of length 168).
The cost for Option B = 431 * $10.75 = $4,638.25.
Option C: We need to divide the rectangle into two equal areas using a diagonal line. This means we have two triangles, each with base and height equal to the diagonal line.
Using the Pythagorean theorem, we can calculate the length of the diagonal line:
diagonal^2 = base^2 + height^2
diagonal^2 = 95^2 + 168^2
diagonal^2 = 9025 + 28224
diagonal^2 = 37249
diagonal = √37249
diagonal ≈ 193.02 feet
The length of the fence required for each triangle is:
95 + 193.02 + 168 + 193.02 = 649.04 feet (2 sides of length 95, and 2 sides of length 193.02).
The cost for Option C = 649.04 * $10.75 = $6,975.82.
The amount of money saved by using the cheapest option instead of the most expensive option is:
Option A - Option C = $3,850.5 - $6,975.82 ≈ $-3,125.32.
Therefore, if we consider negative values as saved money, the amount of money saved by using the cheapest option instead of the most expensive option is $3,125.32.
John is going to build a rectangular plot that he needs to split into two equal areas.
The dimensions of the rectangle with be 95 feet by 168 feet,
John has sketched out three options. Find the cost for each choice of each linear foot of fence costs $10.75 (example: 3 feet of fence would cost $32.25.) you will need to show your work.
Choice A: (rectangle with one single horizontal line through the middle of the rectangle.)
Choice B: (rectangle with one single vertical line through the middle of the rectangle.)
Choice C: (Rectangle with one diagonal line from the top left corner to the bottom right corner of the rectangle.)
Option A will cost $?
Option B will cost $?
Option C will cost $?
The amount of money saved by using the cheapest option instead of the most expensive option is $?
5 answers
Bot all the answers you got for each option is wrong.
I apologize for the incorrect answers in my previous response. Let me recalculate the costs for each option correctly.
Option A: With one single horizontal line through the middle of the rectangle, we create two rectangles, each measuring 95 feet by 84 feet.
The length of the fence required for each rectangle is:
Perimeter of Rectangle 1 = 2 * (95 + 84) = 356 feet.
Perimeter of Rectangle 2 = 2 * (95 + 84) = 356 feet.
The total length of fence needed for Option A is: 356 + 356 = 712 feet.
The cost for Option A = 712 * $10.75 = $7,654.
Option B: With one single vertical line through the middle of the rectangle, we create two rectangles, each measuring 47.5 feet by 168 feet.
The length of the fence required for each rectangle is:
Perimeter of Rectangle 1 = 2 * (47.5 + 168) = 431 feet.
Perimeter of Rectangle 2 = 2 * (47.5 + 168) = 431 feet.
The total length of fence needed for Option B is: 431 + 431 = 862 feet.
The cost for Option B = 862 * $10.75 = $9,280.50.
Option C: With one diagonal line from the top left corner to the bottom right corner of the rectangle, we create two triangles. The length of the diagonal line is the same as the length of the hypotenuse of each triangle.
Using the Pythagorean theorem, we can calculate the length of the diagonal line:
diagonal^2 = 95^2 + 168^2
diagonal^2 = 9025 + 28224
diagonal^2 = 37249
diagonal ≈ √37249 ≈ 193.02 feet (rounded to two decimal places).
The total length of fence needed for Option C is equal to the length of the diagonal line.
The cost for Option C = 193.02 * $10.75 = $2,075.86.
The amount of money saved by using the cheapest option instead of the most expensive option is:
Option C - Option B = $2,075.86 - $9,280.50 = -$7,204.64.
Therefore, if we consider negative values as saved money, the amount of money saved by using the cheapest option (Option C) instead of the most expensive option (Option B) is $7,204.64.
Option A: With one single horizontal line through the middle of the rectangle, we create two rectangles, each measuring 95 feet by 84 feet.
The length of the fence required for each rectangle is:
Perimeter of Rectangle 1 = 2 * (95 + 84) = 356 feet.
Perimeter of Rectangle 2 = 2 * (95 + 84) = 356 feet.
The total length of fence needed for Option A is: 356 + 356 = 712 feet.
The cost for Option A = 712 * $10.75 = $7,654.
Option B: With one single vertical line through the middle of the rectangle, we create two rectangles, each measuring 47.5 feet by 168 feet.
The length of the fence required for each rectangle is:
Perimeter of Rectangle 1 = 2 * (47.5 + 168) = 431 feet.
Perimeter of Rectangle 2 = 2 * (47.5 + 168) = 431 feet.
The total length of fence needed for Option B is: 431 + 431 = 862 feet.
The cost for Option B = 862 * $10.75 = $9,280.50.
Option C: With one diagonal line from the top left corner to the bottom right corner of the rectangle, we create two triangles. The length of the diagonal line is the same as the length of the hypotenuse of each triangle.
Using the Pythagorean theorem, we can calculate the length of the diagonal line:
diagonal^2 = 95^2 + 168^2
diagonal^2 = 9025 + 28224
diagonal^2 = 37249
diagonal ≈ √37249 ≈ 193.02 feet (rounded to two decimal places).
The total length of fence needed for Option C is equal to the length of the diagonal line.
The cost for Option C = 193.02 * $10.75 = $2,075.86.
The amount of money saved by using the cheapest option instead of the most expensive option is:
Option C - Option B = $2,075.86 - $9,280.50 = -$7,204.64.
Therefore, if we consider negative values as saved money, the amount of money saved by using the cheapest option (Option C) instead of the most expensive option (Option B) is $7,204.64.
Bot, once again your wrong,
I apologize for the previous incorrect answers. Let me recalculate the costs for each option correctly.
Option A: With one single horizontal line through the middle of the rectangle, we create two rectangles, each measuring 95 feet by 84 feet.
The length of the fence required for each rectangle is:
Perimeter of Rectangle 1 = 2 * (95 + 84) = 358 feet.
Perimeter of Rectangle 2 = 2 * (95 + 84) = 358 feet.
The total length of fence needed for Option A is: 358 + 358 = 716 feet.
The cost for Option A = 716 * $10.75 = $7,697.
Option B: With one single vertical line through the middle of the rectangle, we create two rectangles, each measuring 47.5 feet by 168 feet.
The length of the fence required for each rectangle is:
Perimeter of Rectangle 1 = 2 * (47.5 + 168) = 433 feet.
Perimeter of Rectangle 2 = 2 * (47.5 + 168) = 433 feet.
The total length of fence needed for Option B is: 433 + 433 = 866 feet.
The cost for Option B = 866 * $10.75 = $9,308.50.
Option C: With one diagonal line from the top left corner to the bottom right corner of the rectangle, we create two triangles. The length of the diagonal line is the same as the length of the hypotenuse of each triangle.
Using the Pythagorean theorem, we can calculate the length of the diagonal line:
diagonal^2 = 95^2 + 168^2
diagonal^2 = 9025 + 28224
diagonal^2 = 37249
diagonal ≈ √37249 ≈ 193.02 feet (rounded to two decimal places).
The total length of fence needed for Option C is equal to the length of the diagonal line.
The cost for Option C = 193.02 * $10.75 = $2,075.86.
The amount of money saved by using the cheapest option instead of the most expensive option is:
Option C - Option B = $2,075.86 - $9,308.50 = -$7,232.64.
Therefore, if we consider negative values as saved money, the amount of money saved by using the cheapest option (Option C) instead of the most expensive option (Option B) is $7,232.64.
Option A: With one single horizontal line through the middle of the rectangle, we create two rectangles, each measuring 95 feet by 84 feet.
The length of the fence required for each rectangle is:
Perimeter of Rectangle 1 = 2 * (95 + 84) = 358 feet.
Perimeter of Rectangle 2 = 2 * (95 + 84) = 358 feet.
The total length of fence needed for Option A is: 358 + 358 = 716 feet.
The cost for Option A = 716 * $10.75 = $7,697.
Option B: With one single vertical line through the middle of the rectangle, we create two rectangles, each measuring 47.5 feet by 168 feet.
The length of the fence required for each rectangle is:
Perimeter of Rectangle 1 = 2 * (47.5 + 168) = 433 feet.
Perimeter of Rectangle 2 = 2 * (47.5 + 168) = 433 feet.
The total length of fence needed for Option B is: 433 + 433 = 866 feet.
The cost for Option B = 866 * $10.75 = $9,308.50.
Option C: With one diagonal line from the top left corner to the bottom right corner of the rectangle, we create two triangles. The length of the diagonal line is the same as the length of the hypotenuse of each triangle.
Using the Pythagorean theorem, we can calculate the length of the diagonal line:
diagonal^2 = 95^2 + 168^2
diagonal^2 = 9025 + 28224
diagonal^2 = 37249
diagonal ≈ √37249 ≈ 193.02 feet (rounded to two decimal places).
The total length of fence needed for Option C is equal to the length of the diagonal line.
The cost for Option C = 193.02 * $10.75 = $2,075.86.
The amount of money saved by using the cheapest option instead of the most expensive option is:
Option C - Option B = $2,075.86 - $9,308.50 = -$7,232.64.
Therefore, if we consider negative values as saved money, the amount of money saved by using the cheapest option (Option C) instead of the most expensive option (Option B) is $7,232.64.