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Difficulty: MediumPerimeter and Fencing Problems

A logistics company is securing an L-shaped equipment depot with a chain-link fence. The facility has a 120-foot southern border, a 90-foot western border, a 75-foot northern border, and a 45-foot eastern border. The remaining two inner boundary walls connect the northern and eastern borders to complete the L-shape. The entire perimeter will be fenced except for a 15-foot wide entrance gate on the southern border. If the fencing material costs 2525 per yard, what is the total cost of the fencing?

  1. A
    $2,625
  2. $3,375Answer
  3. C
    $10,125
  4. D
    $24,375

Answer

The total cost of the fencing is $3,375.
The correct answer is found by first determining the missing inner dimensions of the L-shape (120 - 75 = 45 feet, and 90 - 45 = 45 feet) to find the total 6-sided perimeter (420 feet). After subtracting the 15-foot gate, 405 feet of fencing is needed. Converting this to yards by dividing by 3 gives 135 yards. Multiplying 135 yards by the 25peryardcostresultsin25 per yard cost results in 3,375.

Step-by-Step Solution

1
Calculate the lengths of the two missing inner boundaries.
Inner horizontal border = 120 - 75 = 45 feet. Inner vertical border = 90 - 45 = 45 feet.
All six sides of the L-shape are needed to find the total perimeter. The missing sides are found by subtracting the known parallel outer edges.
2
Calculate the total perimeter of the equipment depot.
120 + 90 + 75 + 45 + 45 + 45 = 420 feet.
The perimeter is the total length of the continuous boundary line enclosing the facility.
3
Subtract the width of the entrance gate from the total perimeter.
420 - 15 = 405 feet.
The 15-foot gate opening does not require fencing material, so it must be removed from the total.
4
Convert the required fencing from feet to yards.
405 / 3 = 135 yards.
The fencing cost is provided in yards, so the perimeter measurement must match the pricing unit.
5
Calculate the total cost of the fencing material.
135 \times 25 = 3,375 dollars.
Multiplying the total yards of fencing by the cost per yard gives the final price.

Key Concept

Calculating the perimeter of composite rectilinear shapes, subtracting non-fenced gaps, and applying unit conversions for total cost.
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Topics

Perimeter and Fencing Problems

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