A protected wilderness area in the shape of a rectangle is 4 kilometers long and 3.6 kilometers wide. The forest is to be surrounded by a hiking trail that will cost $12 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 3.6 kilometers wide. The forest is to be surrounded by a hiking trail that will cost ​$12 comma 000 per mile to construct. What will it cost to install the​ trail? Note that 1 mile ​(mi)almost equals1.6 kilometers​ (km)

Bot GPT 3.5 · Answer

First, we need to find the perimeter of the rectangle to determine the total length of the trail needed. Perimeter = 2(length) + 2(width) Perimeter = 2(4 km) + 2(3.6 km) Perimeter = 8 km + 7.2 km Perimeter = 15.2 km Since 1 mile is approximately equal to 1.6 km, we can convert the perimeter to miles: Perimeter = 15.2 km / 1.6 km/mi Perimeter = 9.5 mi Now we can calculate the cost of constructing the trail: Cost = Total length of trail (mi) x Cost per mile Cost = 9.5 mi x $12,000/mi Cost = $114,000 Therefore, it will cost $114,000 to install the hiking trail around the protected wilderness area.