The length of a rectangular park is twice its breadth. A pathway of uniform…
2025
The length of a rectangular park is twice its breadth. A pathway of uniform width 4 m runs across the park parallel to its breadth, and the area of this pathway is 352 m2. Find the length of the park (in metres).
- A.
92
- B.
180
- C.
184
- D.
176
- E.
88
Attempted by 6 students.
Show answer & explanation
Correct answer: D
Concept
A pathway of uniform width laid across a rectangle, parallel to one side, is itself a rectangle. Its area equals its width multiplied by the side it spans. So for a strip parallel to the breadth, Area = width × breadth. Combined with a stated relation between length and breadth, this fixes both dimensions.
Application
Let the breadth of the park be b metres. The length is twice the breadth, so length = 2b.
A pathway of width 4 m runs parallel to the breadth, so it spans the full breadth b. Its area = 4 × b.
Set this equal to the given area: 4 × b = 352.
Solve for the breadth: b = 352 ÷ 4 = 88 m.
Length = 2b = 2 × 88 = 176 m.
Cross-check
With breadth 88 m, a 4 m strip across it covers 4 × 88 = 352 m2, matching the given pathway area, and the length 176 m is exactly twice 88 m. Both conditions hold, so the length is 176 m.