A path 2 m long and 1 m broad is constructed around a rectangular ground of dimensions 120 m and 90 m respectively. Find the area of the path
Answers
A path 2 m long and 1 m broad is constructed around a rectangular ground of dimensions 120 m and 90 m respectively, then the area of the path is 608 m² or 668 m².
Step-by-step explanation:
From the measurement of the path given 2m length and 1 m broad is not a clear statement, it should be given in terms of wide or broad. Therefore, to get the area of the path, we have to consider two cases which are as follows:
Case 1: Taking 2 m wide on the side of 120 m and 1 m broad on the side of 90 m.
Length of the rectangular ground, l = 120 m
Breadth of the rectangular ground, b = 90 m
∴ Area of the rectangular ground = l * b = 120 * 90 = 10800 m²
Now,
Length of the ground including the path, L = 120 + (2*2) = 124 m
Breadth of the ground including the path, B = 90 + (1*2) = 92 m
∴ Area of the rectangular ground including the path = L * B = 124 * 92 = 11408 m²
Thus,
The area of the path,
= [Area of the rectangular ground including the path] – [Area of the rectangular ground]
= 11408 – 10800
= 608 m²
Case 2: Taking 1 m wide on the side of 120 m and 2 m broad on the side of 90 m.
Length of the ground including the path, L = 120 + (1*2) = 122 m
Breadth of the ground including the path, B = 90 + (2*2) = 94 m
∴ Area of the rectangular ground including the path = L * B = 122 * 94 = 11468 m²
Thus,
The area of the path,
= [Area of the rectangular ground including the path] – [Area of the rectangular ground]
= 11468 – 10800
= 668 m²
Hope this is helpful!!!!!