Answer: the length of the rectangle is 100m and the breadth is 80m
Explanation:
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + breadth)
Let the length of the initial rectangle be and the breadth of the initial rectangle be b
The perimeter of a rectangle is 360m. Therefore,
2(l + b) = 360
l + b = 180
If its length is decreased by 20 %, the new length would be l - 0.2l = 0.8l
its breadth is increased by 25%, the new breadth would be b + 0.25b = 1.25b
we get the same perimeter. Therefore
2(0.8l + 1.25b) = 360
0.8l + 1.25b = 180 - - - - - - - 1
Substituting l = 180 - b into equation 1,it becomes
0.8(180 - b) + 1.25b = 180
144 - 0.8b + 1.25b = 180
- 0.8b + 1.25b = 180 - 144
0.45b = 36
b = 36/0.45 = 80
Substituting b = 80 into l = 180 - b, it becomes
l = 180 - 80 = 100