Question

at your citys council meeting, you hear a proposal for a hiking trail to surround a rectangular area with width 3 km and length 4 km. the trail construction costs $10,000 per mile. you want to double - check the total cost proposed. which strategy is a good first step to verifying the proposal?
multiply the cost per mile by the width
multiply the length by width
draw a picture
add the length and width

Explanation:

Step1: Analyze the problem nature

The problem is about calculating the cost of a hiking - trail around a rectangular area. The cost is per mile, and we need to find the perimeter (since the trail is around the rectangle). A good first step in geometry - related problems (where we deal with shapes like rectangles) is to visualize. Drawing a picture helps in understanding the shape (a rectangle with length \(l = 4\) km and width \(w=3\) km) and identifying that we need to calculate the perimeter.

Step2: Evaluate other options

• Multiplying the cost per mile by the width: The cost is per unit length (mile) of the trail. The width is just one side of the rectangle. This operation does not give the total length of the trail.
• Multiplying the length by the width: This gives the area of the rectangle (\(A=l\times w\)), but we need the perimeter (length of the trail), not the area.
• Adding the length and width: This gives \(l + w\), but the perimeter of a rectangle is \(P=2(l + w)\). Just adding \(l\) and \(w\) is an incomplete step for finding the perimeter.

Answer:

Draw a picture.