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Difficulty: MediumPerimeter and Fencing Problems

A renewable energy company is installing a chain-link fence around a newly constructed rectangular solar farm. The solar farm measures 120120 yards in length and 8585 yards in width. The fence will enclose the entire perimeter, with the exception of two access gates that each measure 55 yards wide. If the fencing material costs $22\$22 per linear yard, what is the total cost of the fencing material in dollars?

Answer: 8800 $

Answer

The total cost of the fencing material is 8800 dollars.
The total perimeter of the solar farm is 410410 yards (120+120+85+85120 + 120 + 85 + 85). Subtracting the 1010 yards for the two 55-yard gates leaves 400400 yards of fencing to be installed. Multiplying 400400 yards by the $22\$22 per yard cost gives a total of $8800\$8800.

Step-by-Step Solution

1
Calculate the total perimeter of the rectangular solar farm.
P=2×(120+85)=2×205=410P = 2 \times (120 + 85) = 2 \times 205 = 410 yards.
The perimeter formula for a rectangle is P=2(L+W)P = 2(L + W), which represents the total boundary length before any openings are considered.
2
Determine the total width of the two access gates.
2×5=102 \times 5 = 10 yards.
Since there are two gates and each is 55 yards wide, their combined width must be subtracted from the total perimeter.
3
Calculate the actual length of fencing needed.
410−10=400410 - 10 = 400 yards.
The fencing covers the perimeter minus the space left open for the access gates.
4
Calculate the total cost of the fencing material.
400×22=8800400 \times 22 = 8800.
Multiplying the total yards of fencing by the cost per yard gives the total cost in dollars.

Key Concept

Calculating the perimeter of a rectangle, subtracting openings, and finding the total cost based on a unit price.
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Topics

Perimeter and Fencing Problems

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