GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementHard
A landscape architect is designing a path through a park. The path will be 3 feet wide and will follow the perimeter of a rectangular grassy area that measures 50 feet by 100 feet. If the path is to be paved with stones that cover 1.5 square feet each, approximately how many stones are needed for the path?
- A600 stones
- B200 stones
- C100 stones
- D800 stones
Show answer & explanationAnswer & explanation
Correct answer: A. 600 stones
First, calculate the perimeter of the rectangular grassy area. Then, multiply the perimeter by the path's width to find the total area of the path. Finally, divide the path's area by the coverage of each stone and round up.
Why the other options are wrong
- B. This is an underestimation, likely from an arithmetic error or misunderstanding of path area.
- C. This is a significant underestimation, possibly due to calculating only perimeter or area of the grassy area.
- D. This is an overestimation, possibly from incorrect area calculation or division.
Area of a Path
The area of a uniform strip surrounding a shape, calculated by multiplying the perimeter of the inner shape by the path's width.
- Assumes path is on the outside or inside of the perimeter
- Formula: Perimeter × Width (for a uniform path)
- Requires careful attention to whether the path is added to or subtracted from dimensions
Memory trick: Perimeter Path Paves Perfectly