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Answer :
Final answer:
The total cost of constructing the fence is calculated by determining the cost of labor and materials. After calculating the perimeter of the lot for labor costs and the area of the fence for material costs, the total cost is found to be $3504.50, corresponding with option D.
Explanation:
To calculate the total cost of constructing a fence, we need to determine the cost of labor (erecting the fence) and the cost of materials. The labor cost is based on the perimeter of the lot, while the material cost depends on the area of the fence surface.
First, let's calculate the perimeter of the lot, which is the distance around the lot:
Perimeter = (2 × length) + (2 × width)
Perimeter = (2 × 90 ft) + (2 × 175 ft)
Perimeter = 180 ft + 350 ft
Perimeter = 530 ft
Now we calculate the labor cost:
Labor cost = Perimeter × Cost per linear foot
Labor cost = 530 ft × $1.25/ft
Labor cost = $662.50
For the materials, we need to find the area of the fence surface. The height of the fence is 6 feet 6 inches (or 6.5 feet), so the area is:
Area = Perimeter × Height
Area = 530 ft × 6.5 ft
Area = 3445 square ft
The material cost is then:
Material cost = Area × Cost per square foot
Material cost = 3445 sq ft × $0.825/sq ft
Material cost = $2842.125
Adding both labor and material costs gives us the total cost:
Total cost = Labor cost + Material cost
Total cost = $662.50 + $2842.125
Total cost = $3504.625
However, since there is no option matching $3504.625 exactly and costs are typically rounded to the nearest cent, the closest answer is $3504.50 which corresponds with option D.
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