A path around a garden — Mensuration Aptitude Question
A path around a garden: A rectangular garden 50 m × 30 m is surrounded by a path 2 m wide on the outside. Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
A rectangular garden 50 m × 30 m is surrounded by a path 2 m wide on the outside. What is the area of the path?
Options
- 316 m²
- 336 m²
- 356 m²
- 376 m²
Show the answer and the worked solution
Correct answer: B. 336 m²
Worked solution
- Outer rectangle = 54 × 34 = 1,836 m².
- Garden = 50 × 30 = 1,500 m².
- Path = 1,836 − 1,500 = 336 m².
Answer: 336 m².
The idea
An outside path adds twice its width to each dimension; an inside path subtracts twice. Everything else is the difference of two rectangles.
Shortcut. Path area = garden perimeter × width + four corner squares: 160 × 2 + 4 × 4 = 336.
Common trap. 316 m² — forgetting the four 2 × 2 corners gives 320, and 316 is the nearest option to it; the corners add 16, making 336.