A path inside a rectangular field — Aptitude Question
A path inside a rectangular field: A path 2 m wide runs inside a rectangular field 30 m × 20 m, along its boundary. Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
A path 2 m wide runs inside a rectangular field 30 m × 20 m, along its boundary. What is the area of the path?
Options
- 176 m²
- 184 m²
- 192 m²
- 200 m²
Show the answer and the worked solution
Correct answer: B. 184 m²
Worked solution
- Outer area = 30 × 20 = 600 m².
- Inner rectangle (path removed on all sides): (30 − 4) × (20 − 4) = 26 × 16 = 416 m².
- Path = 600 − 416 = 184 m².
Answer: 184 m².
The idea
A border path is the difference of two rectangles; the width comes off twice from each dimension. For an outside path, add 2w instead.
Shortcut. Path area = 2w(l + b) − 4w² = 4 × 50 − 16 = 184 m².
Common trap. 200 m² — laying four 2 m strips along the full sides (2 × 2 × 50) and so counting the four 2 × 2 corners twice; subtract 16 m².