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You want to buy a triangular lot measuring 1380 feet by 1830 feet by 2490 feet. The cost of the land is $62,000. What is the price of the land per acre?

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

$

Answer :

Final answer:

The final price per acre comes to approximately $2205.56. To find the price of the triangular lot per acre, calculate its area using Heron's formula, convert the area from square feet to acres, and then divide the total cost of the land by the number of acres.

Explanation:

The question deals with calculating the price of a triangular lot per acre. To find the area of the triangular lot, we can use Heron's formula, which requires knowing the semi-perimeter (s = (a+b+c)/2) where a, b, and c are the lengths of the sides of the triangle. The area (A) is given by the square root of s*(s-a)*(s-b)*(s-c). Once we have the area in square feet, we can convert it to acres by dividing by 43,560 (the number of square feet in one acre). With the area in acres, we can calculate the price per acre by dividing the total cost of the land by the number of acres.

First, we calculate the semi-perimeter (s):

s = (1380 + 1830 + 2490) / 2 = 2850

Next, we use Heron's formula to find the area:

A = √(s(s-a)(s-b)(s-c))
A = √(2850(2850-1380)(2850-1830)(2850-2490))
A = √(2850*1470*1020*360) = √(1500846000000)
A = 1224762.28 square feet

To find the area in acres, we divide by 43,560:

Acres = 1224762.28 / 43,560 ≈ 28.112 acres

To calculate the price per acre, we divide the cost by the number of acres:

Price per acre = $62,000 / 28.112 ≈ $2205.56

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Rewritten by : Barada