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Chapter 5: Problem 61

You want to buy a triangular lot measuring 510 yards by 840 yards by 1120 yards. The price of the land is \(\$ 2000\) per acre. How much does the land cost? (Hint: 1 acre \(=4840\) square yards)

Short Answer

Expert verified
After performing all calculations, the cost of the land should be your final answer in dollars.

Step by step solution

01

Calculate Semi-Perimeter of Triangle

The semi-perimeter (s) of a triangle whose sides are a, b, c is calculated as \(s = \frac{a + b + c}{2}\). Here, \(a = 510 yards\), \(b = 840 yards\) and \(c = 1120 yards\). Plug these values into the formula and calculate s.
02

Calculate Area of Triangle Using Heron's Formula

Once the semi-perimeter is found, the area (A) of the triangle can be calculated using Heron's formula, which is \(A = \sqrt{s(s - a)(s - b)(s - c)}\). Substitute the values of s, a, b, and c in the formula and calculate the area.
03

Convert Area from Square Yards to Acres

The given area will be in square yards. To convert this to acres, use the conversion 1 acre = 4840 square yards. Therefore, \(A_{acres} = \frac{A_{yards}}{4840}\). Substitute the calculated value of A in square yards in the formula and find the area in acres.
04

Calculate the Cost of Land

Finally, to find the cost of the land, multiply the area in acres by the cost per acre ($2000). The final answer will be in dollars.

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