The area and perimeter of a rectangle are equal. If the length is l and the breadth is b.
2(l + b) = l*b
This is possible if l + b = (l*b)/2
The above equation can have infinite solutions, for example
l = 4 => b = 4
l = 8 => b = 8/3
l = 16 => b = 16/7
As there is only equation relating the two variables l and b, there are an infinite number of solutions.
Let the length of rectangle be l and breadth be b
The given condition can be expressed in equation as following
: 2(l+b) = lb
Because length and breadth are not necessarily integers, there would be an infinite number of solution for (l-2, b-2) which sastisfies the equation above. Therefore, number of solution (l,b) should be in infinite number.