Question

a protected wilderness area in the shape of a rectangle is 3 kilometers long and 3 kilometers wide. the forest is to be surrounded by a hiking trail that will cost $12,000 per mile to construct. what will it cost to install the trail? note that 1 mile (mi) ≈ 1.6 kilometers (km)
it will cost $□ to install the trail.
(type an integer or a decimal.)

Explanation:

Step1: Calculate the perimeter of the rectangle

The formula for the perimeter of a rectangle is \(P = 2(l + w)\), where \(l = 3\) km and \(w = 3.3\) km.
\(P=2(3 + 3.3)=2\times6.3 = 12.6\) km.

Step2: Convert kilometers to miles

Since \(1\) mile\(\approx1.6\) kilometers, then the number of miles \(m=\frac{12.6}{1.6}=7.875\) miles.

Step3: Calculate the cost

The cost per mile is \(\$12000\). So the total cost \(C = 12000\times7.875\).
\(C=12000\times\frac{7.875}{1}=\frac{12000\times7875}{1000}=12\times7875 = 94500\)

Answer:

\(94500\)