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Difficulty: HardPerimeter and Fencing Problems

A military logistics facility is upgrading the security fence around a rectangular motor pool. The motor pool is 5050 yards long and 8484 feet wide. The new design requires leaving a 2424-foot gap for a main vehicle gate and two separate 33-foot gaps for pedestrian access. The security fencing is purchased in pre-assembled panels that are 7272 inches long each. If each panel costs $120\$120, what is the total cost of the fencing panels needed to enclose the motor pool?

Answer: 8760 dollars

Answer

8760 dollars
The correct calculation requires converting all linear measurements to a common unit (feet), calculating the perimeter of the rectangle, subtracting the required gaps for the gates, dividing the remaining length by the panel length to find the total number of panels, and finally multiplying by the cost per panel.

Step-by-Step Solution

1
Convert yards and inches to feet.
Length is 150 feet; panel length is 6 feet.
To ensure consistency in perimeter and material calculations before determining the number of panels.
2
Calculate the full perimeter of the rectangular motor pool.
468 feet.
To find the total boundary length before accounting for the gaps left for gates.
3
Subtract the total width of the gate gaps from the full perimeter.
438 feet.
Because fencing panels are not installed where the vehicle and pedestrian gates are located.
4
Divide the required fencing length by the length of a single panel.
73 panels.
To find how many discrete 6-foot sections make up the 438-foot fence line.
5
Multiply the number of panels by the cost per panel.
$8,760.
To find the final total price of purchasing the required materials.

Key Concept

Calculating perimeter with unit conversions and subtracting gaps to find total material cost.
Estimated Time:2m 0s
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Topics

Perimeter and Fencing Problems

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