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Answer :
Final answer:
To calculate the cost of the fence, the perimeter of the lot is found to be 530 feet and the fence area is 3445 square feet. The erecting cost totals $1192.50 and the material cost is $6273.90, summing up to a total cost of $7466.40.
Explanation:
The question asks us to calculate the total cost to build a fence that is 6 feet 6 inches tall around a rectangular lot measuring 90 feet by 175 feet, with specific costs provided for both labor ($2.25 per linear foot) and materials ($1.82 per square foot of fence).
To answer this question, we will need to calculate the total linear feet of the fence needed and the total square footage of the fence. The perimeter (total linear feet) of a rectangle is given by the formula P = 2(length + width). Hence, the lot perimeter is: P = 2( 90 + 175 ) = 530 feet.
The total square footage of the fence can be determined by multiplying the total linear feet of the fence by its height. Since the fence height needs to be converted to feet, 6 feet 6 inches is equal to 6.5 feet. So, the total area is: A = 530 * 6.5 = 3445 square feet.
Now we can calculate the costs. Erecting the fence will be: Erecting cost = $2.25 * 530 = $1192.50.
And the cost for materials will be: Material cost = $1.82 * 3445 = $6273.90.
The total cost is the sum of both the erecting cost and the material cost: Total cost = $1192.50 + $6273.90 = $7466.40.
The total cost to build the fence around the lot is therefore $7466.40.
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