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You want to buy a triangular lot measuring 1370 feet by 1860 feet by 2410 feet. The price of the land is $2200 per acre. How much does the land cost?

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

Answer :

Final answer:

The problem requires using Heron's formula to solve for the area of a triangle then converting the area in square feet to acres. Once the size of the land in acres is determined, the cost of the land is calculated by multiplying it by the price per acre.

Explanation:

This problem involves the concept of Heron's formula and conversion of square feet to acres. Heron's formula calculates the area of a triangle using the lengths of all three sides. The three sides of the triangle are 1370 feet, 1860 feet, and 2410 feet.

First, we find the semi-perimeter (s) which is equal to (a+b+c)/2. Substituting the values, the semi-perimeter is 2410+1860+1370/2 = 2820 feet. Next, we apply Heron's formula to find the area of the triangle which is √[s(s-a)(s-b)(s-c)]. Substituting the known values results to √[2820(2820-2410)(2820-1860)(2820-1370)], which gives us the answer in square feet.

Now, we need to convert the result from square feet to acres. As given, 1 acre is equal to 43,560 square feet. After converting, you can find the total cost by multiplying this area by its rate per acre ($2200) to obtain the cost of land.

Learn more about Area Calculation here:

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