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Zorluk: ZorPerimeter and Fencing Problems

A homeowner is enclosing a rectangular garden with a new fence. The garden has a length of 55 yards and a width of 88 feet. The homeowner will leave a 3636-inch wide opening along one of the sides for a wooden gate. If the fencing material costs $14.50\$14.50 per linear foot, what is the total cost of the fencing material required?

  1. A
    $333.50\$333.50
  2. $623.50\$623.50Cevap
  3. C
    $1,740.00\$1,740.00
  4. D
    $6,235.00\$6,235.00

Cevap

$623.50\$623.50
To find the correct total cost, all dimensions must first be converted to feet (55 yards =15= 15 feet, 3636 inches =3= 3 feet). The perimeter is found by adding all four sides (15+15+8+8=4615 + 15 + 8 + 8 = 46 feet), then subtracting the 33-foot gate opening to determine that exactly 4343 feet of fencing is needed. Multiplying 4343 feet by the $14.50\$14.50 cost per foot yields the correct total of $623.50\$623.50.

Adım Adım Çözüm

1
Convert all given measurements to a single common unit (feet) since the cost is given per linear foot.
Length: 5 yards=15 feet5 \text{ yards} = 15 \text{ feet}. Gate width: 36 inches=3 feet36 \text{ inches} = 3 \text{ feet}.
Measurements must be in the same units as the pricing rate to calculate accurate costs.
2
Calculate the total perimeter of the rectangular garden.
P=2×(Length+Width)=2×(15+8)=2×23=46 feetP = 2 \times (\text{Length} + \text{Width}) = 2 \times (15 + 8) = 2 \times 23 = 46 \text{ feet}.
The perimeter represents the total outline of the garden before accounting for the gate.
3
Subtract the width of the gate opening from the total perimeter.
46 feet−3 feet=43 feet46 \text{ feet} - 3 \text{ feet} = 43 \text{ feet}.
Fencing material is not needed across the opening where the wooden gate will be installed.
4
Multiply the required length of fencing by the cost per linear foot.
43 feet×$14.50/foot=$623.5043 \text{ feet} \times \$14.50/\text{foot} = \$623.50.
This provides the final total monetary cost for the required material.

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Perimeter and Unit Conversion
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Perimeter and Fencing Problems

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