let length and breadth be x and y respectively.
perimeter = 20 => 2(x+y) = 20 => x+y = 10
Area = x*y = x(10-x)
Differentiation method:
Area = f(x) = x(10-x) = 10x-x^2
first find first derivative of f(x):
f'(x) = 10-2x
second derivative, f''(x) = -2 < 0, hence f(x) has a maximum value at 'x' when f'(x) = 0
=> 10-2x = 0 => x = 5;
The maximum value of f(x) is at x=5 and is f(5) = 5(10-5) = 25 units
The maximum possible area is 25
Hence option III, which is 26 is ruled out. And options I and II are possible.
Answer "C"