Chapter 6.2, Problem 60E

To determine

The cost of the land.

Answer to Problem 60E

The total cost is $62340.7.

Explanation of Solution

Given:

The triangular lot of 1350 feet by 1860 feet by 2490 feet size. The price of the land is $2200 per acre.

Considering the three sides of the triangular parcel:

  $\begin{array}{l}a=2490\\ b=1860\\ c=1350\end{array}$

Using the Heron’s formula evaluating the area of the land:

First, the value of the s is evaluated as:

  $\begin{array}{l}s=\frac{a+b+c}{2}\\ =\frac{2490+1860+1350}{2}\\ =2850\end{array}$

Now, from the Heron’s formula:

  $\begin{array}{l}\text{Area=}\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ =\sqrt{2850\left(2850-2490\right)\left(2850-1860\right)\left(2850-1350\right)}\\ =1234345.98\text{square feet}\end{array}$

Now, the land per square feet is evaluated as:

  $\begin{array}{l}\frac{1234345.98}{43560}=28.33\\ \text{Hence,}\\ \text{cost=28}\text{.33}\times \text{2200}\\ \text{ =\$62340}\text{.70}\end{array}$

Therefore, the total cost is $62340.7.