These problems involve finding the width of a path around a flower bed.
📘 Example ①
A path of the same width x m was built around a rectangular flower bed measuring 10 m long and 8 m wide. The total area, including the path, became 168m². Find x.
Answer:(10+2x)(8+2x) = 168。Expansion: 80 + 36x + 4x² = 168 → 4x² + 36x − 88 = 0 → x² + 9x − 22 = 0 → (x+11)(x−2) = 0 → x = 2m
A path of the same width x m was built around a rectangular flower bed measuring 10 m long and 8 m wide. The total area, including the path, became 168m². Find x.
Answer:(10+2x)(8+2x) = 168。Expansion: 80 + 36x + 4x² = 168 → 4x² + 36x − 88 = 0 → x² + 9x − 22 = 0 → (x+11)(x−2) = 0 → x = 2m
💡 Key Point
- Since there is a path on both sides, add 2x to each side
- The path width is positive → discard the negative solution
Practice Problems
- A path of width x m was built around a flower bed measuring 6 m long and 4 m wide, making the total area 48m². Find x.
Answers and Explanations
- Answer:x = 1m。(6+2x)(4+2x)=48 → 4x²+20x+24=48 → 4x²+20x−24=0 → x²+5x−6=0 → (x+6)(x−1)=0 → x=1（x>0）。