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There is a rectangular path just inside a rectangular park. The width of the path is 2 cm. If the length of the park is decreased by 4 cm, it becomes a square. The area of the rectangle is 1\(\tfrac{1}{3}\) times the area of the path. From the above information, which of the following can be found out? (i) Area of the path (ii) Length of the park (iii) Sum of the perimeter of the rectangular park and the perimeter of the path (both external and internal perimeter) A) only (ii) B) only (ii) and (iii) C) only (i) and (iii) D) all of the above E) only (iii)

1. only (ii)
2. only (ii) and (iii)
3. only (i) and (iii)
4. all of the above
5. only (iii)

Correct answer: all of the above

Solution

Let the park be \(L \times B\), and since decreasing the length by 4 cm makes it a square, we get \(L-4=B\). The path width is 2 cm, so the inner rectangle is \((L-4)\times(B-4)\). Using the given area ratio, both dimensions can be determined, and then the path area and perimeters can also be found.

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