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Question

Difficulty: MediumPerimeter and Fencing Problems

An event coordinator is setting up a temporary security perimeter for an outdoor festival. The secured VIP zone is rectangular, measuring 3030 yards in length and 2020 yards in width. An un-fenced opening of 55 yards must be left on one side for the main entrance gate. If the temporary fencing costs $4.50\$4.50 per linear foot, what is the total cost, in dollars, of the fencing required?

Answer: 1282.5 dollars

Answer

1282.5
The correct total cost is 1282.50.Tofindthis,thefullperimeterofthe30−by−20yardrectangleiscalculatedas100yards.Aftersubtractingthe5−yardopening,95yardsoffencingareneeded.Becausethefencingispricedperfoot,the95yardsmustbeconvertedto285feetbymultiplyingby3.Finally,multiplying285feetbythe1282.50. To find this, the full perimeter of the 30-by-20 yard rectangle is calculated as 100 yards. After subtracting the 5-yard opening, 95 yards of fencing are needed. Because the fencing is priced per foot, the 95 yards must be converted to 285 feet by multiplying by 3. Finally, multiplying 285 feet by the 4.50 per foot cost yields 1282.50.

Step-by-Step Solution

1
Calculate the total perimeter of the rectangular zone in yards.
100 yards
The perimeter represents the total distance around the rectangle before accounting for any openings.
2
Subtract the gate opening from the perimeter.
95 yards
Fencing is not required for the 5-yard entrance gate.
3
Convert the required fencing length from yards to feet.
285 feet
The cost of the fencing is provided per linear foot, so the length must be in feet.
4
Calculate the total cost by multiplying the length in feet by the price per foot.
1282.5
Total cost equals the total amount of material multiplied by the unit price.

Key Concept

Calculating perimeter of a rectangle, adjusting for openings, and converting units for cost calculation.
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Topics

Perimeter and Fencing Problems

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