Solution:
Length = l
Breadth = b
Perimeter = 2(L+b) = 80
=> l+b = 40 .......... (eq 1)
Area = lb = 400 ........... (eq 2)
=> (l+b)2 = (l-b)2 + 4lb
=> 402 = (l-b)2 + 4 x 400 [From eqn 1 & 2)
=> 1600 = (l-b)2 + 1600
=> l-b = 0 .................... (eq 3)
L+b = 40
L-b = 0
2L = 40 => L = 20.
If L=20, then B=20
So, yes ! We can construct a rectangular park of this length which is a square. Square is a Rectangle.