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You want to buy a triangular lot measuring 1340 feet by 1890 feet by 2410 feet. The cost of the land is $62,000. What is the price (in dollars) of the land per acre?

Hint: 1 acre = 43,560 square feet. Round your answer to two decimal places.

Answer :

Final answer:

To find the price of the land per acre, calculate the total area of the triangular lot, convert it to acres, and divide the cost of the land by the number of acres.

Explanation:

To find the price of the land per acre, we first need to calculate the total area of the triangular lot in square feet. We can use Heron's formula to find the area of a triangle with side lengths of 1340, 1890, and 2410 feet. Once we have the total area in square feet, we can convert it to acres by dividing by 43,560. Finally, we divide the cost of the land by the number of acres to obtain the price per acre.

Let's calculate:

Step 1: Calculate the area of the triangle using Heron's formula:

s = (1340 + 1890 + 2410) / 2 = 2820 feet

Area = sqrt(2820(2820-1340)(2820-1890)(2820-2410)) = 1058847.23 square feet

Step 2: Convert square feet to acres:

Area (in acres) = 1058847.23 / 43560 = 24.33 acres (rounded to two decimal places)

Step 3: Calculate the price per acre:

Price per acre = $62,000 / 24.33 acres = $2545.23 per acre (rounded to two decimal places)

Therefore, the price of the land per acre is $2545.23.

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