pre calc question

Question

The lengths of the sides of a triangular parcel of land are approximately 500 feet, 600 feet, and 950 feet. If land is valued at $2000 per acre (1 acre is 43,560 ft2), what is the value of the parcel of land? (Round your answer to the nearest cent.)

Answer 1

Hi Emi, to solve this problem, you can use Heron's formula to find the area of the triangle. Then divide the area by the square feet in one acre to find the total number of acres in the triangle. Last, multiply the number of acres by $2000 to find the value of the land.

 

A = √(p * (p - a) * (p - b) * (p - c))

 

Where:

 

A is the area

 

p represents (a + b + c) / 2, or one have of the perimeter of the triangle.

 

a, b, and c are the lengths of the sides of the triangle.

 

Let a = 500 feet, b = 600 feet, and c = 950 feet.

 

p = (500 + 600 + 950) / 2, or 1025 feet

 

Substitute in the formula:

 

A = √(1025 * (1025 - 500) * (1025 - 600) * (1025 - 950))

 

A ≈ 130968.448 square feet

 

Number of acres: 130968.448 / 43,560 ≈ 3.0066 acres

 

Value of the land: 3.0066 * 2000 ≈ $6013.20

 

Note: 

 

Using a calculator carrying forward each value instead of rounding, the answer comes out as: $6013.24

 

Your answer will depend on the accuracy of your calculator.

 

Questions?