A protected wilderness area in the shape of a rectangle is 4 kilometers long and 3.8 kilometers wide. The forest is to be surrounded by a hiking trail that will cost $10 comma 000 per mile to construct. What will it cost to install the trail? Note that 1 mile (mi)almost equals1.6 kilometers (km)

Question

A protected wilderness area in the shape of a rectangle is 4 kilometers long and 3.8 kilometers wide. The forest is to be surrounded by a hiking trail that will cost ​$10 comma 000 per mile to construct. What will it cost to install the​ trail? Note that 1 mile ​(mi)almost equals1.6 kilometers​ (km)

GPT 3.5 · Answer

To find the cost of installing the hiking trail around the wilderness area, we first need to find the perimeter of the rectangle.

Perimeter = 2(length + width)
Perimeter = 2(4 km + 3.8 km)
Perimeter = 2(7.8 km)
Perimeter = 15.6 km

Since 1 mile is approximately equal to 1.6 kilometers, we need to convert kilometers to miles:
15.6 km / 1.6 km/mi ≈ 9.75 miles

Now we can calculate the total cost of installing the hiking trail:
Cost = 9.75 miles * $10,000/mile
Cost = $97,500

Therefore, it will cost $97,500 to install the trail around the protected wilderness area.