Answer :
Final answer:
To calculate the cost of building a fence, we ascertain the perimeter for installation costs and the total area for material costs. The calculations yield an installation cost of $1,192.50 and a material cost of $12,539.80. The final total cost is $13,732.30, which is not among the provided options.
Explanation:
The subject of this question is Mathematics, specifically dealing with geometric measurements and cost calculations. To find the cost of building a fence around the lot, we need to calculate both the perimeter for the installation cost and the total area for the material cost.
First, we calculate the perimeter of the lot to find out how many linear feet of fencing is needed. The lot is a rectangle, so the perimeter (P) is given by:
P = 2(length + width) = 2(90 feet + 175 feet) = 2(265 feet) = 530 feet
Next, we calculate the cost of erecting the fence at $2.25 per linear foot:
Installation Cost = P × installation rate per foot = 530 feet × $2.25/foot = $1,192.50
Then, we consider the height of the fence which is 6 feet 6 inches, or 6.5 feet, to calculate the total area of the fence. The total area (A) of one side of the fence is given by:
A = Perimeter × Height = 530 feet × 6.5 feet = 3,445 square feet
However, since the fence has two sides, we must double this area. So the total area for both sides is:
Total Area = 2 × A = 2 × 3,445 square feet = 6,890 square feet
Now, we compute the material cost at $1.82 per square foot:
Material Cost = Total Area × material rate per square foot = 6,890 square feet × $1.82/square foot = $12,539.80
Adding both costs together gives us the final cost to build the fence:
Final Cost = Installation Cost + Material Cost = $1,192.50 + $12,539.80 = $13,732.30
Thus, none of the provided options in the question is correct; hence, the correct option is not listed in the final answer.
