There is a rectangular path just inside a rectangular park. Width of the path…
2018
There is a rectangular path just inside a rectangular park. Width of the path is 2 cm. If length of park is decreased by 4 cm then, it becomes a square. Area of the rectangle is 1⅓ times the area of the path.
From the above given information which of the following can be found out.
(i) Area of path
(ii) Length of the park
(iii) Sum of perimeter of the rectangular park and 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)
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Let the park breadth be x cm and length be x + 4 cm. Since the path is 2 cm wide inside the park, the inner rectangle is (x - 4) by x.
The path area is x(x + 4) - x(x - 4) = 8x. Given park area is 1 1/3 times the path area, x(x + 4) = (4/3) x 8x.
This determines the park dimensions, so the path area, length of the park, and required perimeters can all be found.