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Difficulty: MediumPerimeter and Fencing Problems

A homeowner is planning to enclose a rectangular residential lot with a new privacy fence. The lot has a length of 2020 yards and a width of 4545 feet. The fencing material costs $12.50\$12.50 per linear foot. If the homeowner needs to leave a 66-foot opening for a driveway gate, what will be the total cost of the fencing materials?

  1. A
    $255\$255
  2. B
    $1,550\$1,550
  3. $2,550\$2,550Answer
  4. D
    $33,675\$33,675

Answer

The total cost of the fencing materials is $2,550\$2,550.
The correct answer is found by first converting all units to feet. The length of 2020 yards is equal to 6060 feet. The total perimeter of the rectangular lot is 2×(60+45)=2102 \times (60 + 45) = 210 feet. Subtracting the 66-foot gap for the gate leaves 204204 linear feet of fencing required. Multiplying this by the cost of $12.50\$12.50 per foot yields a total cost of $2,550\$2,550.

Step-by-Step Solution

1
Convert the length of the lot from yards to feet.
20 yards×3=60 feet20 \text{ yards} \times 3 = 60 \text{ feet}
All measurements must be in the same unit (feet) because the fencing cost is given per linear foot.
2
Calculate the total perimeter of the rectangular lot.
P=2×(60+45)=2×105=210 feetP = 2 \times (60 + 45) = 2 \times 105 = 210 \text{ feet}
The fencing will go around the entire boundary of the rectangular lot.
3
Subtract the length of the driveway gate from the total perimeter.
210−6=204 feet210 - 6 = 204 \text{ feet}
Fencing material is not needed for the space where the gate will be installed.
4
Calculate the total cost by multiplying the fencing length by the cost per foot.
204×$12.50=$2,550204 \times \$12.50 = \$2,550
The total cost is the required length in feet multiplied by the price per linear foot.

Key Concept

Calculating the perimeter of a rectangle with mixed units and adjusting for an opening.
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Topics

Perimeter and Fencing Problems

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