Examkin

Question

Difficulty: MediumPerimeter and Fencing Problems

A contractor is installing a security perimeter around a rectangular warehouse facility. The facility is 4040 yards long and 2525 yards wide. The fence will include three 1010-foot gates that do not require fencing material. If the fencing costs $18\$18 per yard, what is the total cost of the fencing material required?

  1. A
    $990
  2. B
    $1,800
  3. $2,160Answer
  4. D
    $18,000

Answer

The correct total cost of the fencing material is $2,160.
The total perimeter is found using the formula 2×(L+W)2 \times (L + W), yielding 130130 yards. The three 1010-foot gates have a combined width of 3030 feet, which converts to 1010 yards (30÷330 \div 3). Subtracting the gate width leaves 120120 yards of actual fencing needed. Multiplying this by the cost of $18\$18 per yard yields the total of $2,160\$2,160.

Step-by-Step Solution

1
Calculate the total perimeter of the rectangular facility in yards.
2×(40+25)=1302 \times (40 + 25) = 130 yards
The fencing will go around the entire boundary of the rectangle, which requires the perimeter formula P=2L+2WP = 2L + 2W.
2
Convert the total width of the gates from feet to yards.
3 gates×10 feet/gate=30 feet3 \text{ gates} \times 10 \text{ feet/gate} = 30 \text{ feet}. Since 3 feet=1 yard3 \text{ feet} = 1 \text{ yard}, 30 feet=10 yards30 \text{ feet} = 10 \text{ yards}.
The perimeter and the fencing cost are both in yards, so the gate measurements must match the primary unit.
3
Subtract the gate width from the total perimeter to find the required fencing.
130 yards−10 yards=120 yards130 \text{ yards} - 10 \text{ yards} = 120 \text{ yards}
The sections where the gates are located do not require any fencing material.
4
Calculate the total cost of the fencing material.
120 yards×$18/yard=$2,160120 \text{ yards} \times \$18/\text{yard} = \$2,160
Multiplying the total required yards by the price per yard provides the final monetary cost.

Key Concept

Calculating perimeter of a rectangle, performing unit conversions (feet to yards), and subtracting openings to find total material cost.
Rate this question

Topics

Perimeter and Fencing Problems

More questions from this topic