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 times the area of the path. From the above given information which of the following can be found out. (2 MARKS) (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)
Answers
(D) is the correct option!
Step-by-step explanation:
Given, Width of Path (b) = 2 cm
Let the length of path be L (cm) (Initially when it's rectangular in shape)
Now, Width of Square shaped path (b1) = 2 cm
& Length of Square shaped path (L1) = (L - 4) cm
Since we know that the length and breadth of the square are Equal.
Hence, we can make out that the length of the square (L1) is 2 cm, which equals the breadth.
Now, L - 4 = L1
L = L1 + 4
L = 2 + 4 = 6 cm
Now, Area of rectangular path = 6 x 2 = 12 cm²
New Area of square shaped path = 2 x 2 = 4 cm²
Length of Park = Perimeter of Park = 2(L + b) = 2(6 + 2) = 2 x 8 = 16 cm '''''''(a)
Perimeter of Square shaped Path = 4 x (L1) = 4 x 2 = 8 cm '''''''''''(b)
Sum of (a) & (b) = Sum of perimeter of the rectangular park and perimeter of the path
= 16 + 8 = 24 cm
Hence, we can calculate (d) all of the above