A rectangular park is surrounded by a path of uniform width 2 metres all round…
2023
A rectangular park is surrounded by a path of uniform width 2 metres all round it. The area of the path is 288 sq. metres. The perimeter of the park is :
- A.
142 m
- B.
128 m
- C.
136 m
- D.
118 m
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Correct answer: C
Solution: Find the perimeter of the rectangular park.
Let the park's length and breadth be L and B metres.
The outer rectangle including the path has dimensions (L + 4) by (B + 4) because the path adds 2 m on each side.
Area of the path = (L + 4)(B + 4) - LB = 4(L + B) + 16.
Set this equal to the given path area: 4(L + B) + 16 = 288, so 4(L + B) = 272 and L + B = 68.
Perimeter of the park = 2(L + B) = 2 × 68 = 136 m.
Answer: 136 m.