Given information:
Diagonal of the rectangle = 41 cm
Area of the rectangle = 20 sq. cm

To find: The perimeter of the rectangle

Let's assume the length of the rectangle as 'l' and the breadth of the rectangle as 'b'.

Using the given information, we can form the following equations:

1. Diagonal of a rectangle:
According to the Pythagorean theorem, the square of the diagonal of a rectangle is equal to the sum of the squares of its length and breadth.
So, we have:
l^2 + b^2 = 41^2

2. Area of a rectangle:
The area of a rectangle is given by the product of its length and breadth.
So, we have:
l * b = 20

Solving the equations:

From equation 2, we can express the length (l) in terms of the breadth (b):
l = 20/b

Substituting this value of l in equation 1, we get:
(20/b)^2 + b^2 = 41^2

Simplifying the equation:

400/b^2 + b^2 = 1681
Multiplying through by b^2, we get:
400 + b^4 = 1681b^2

Rearranging the equation:
b^4 - 1681b^2 + 400 = 0

This is a quadratic equation in terms of b^2. Let's solve it using a substitution method:

Let x = b^2
Then, the equation becomes:
x^2 - 1681x + 400 = 0

Now, we can solve this quadratic equation using factorization or the quadratic formula. After solving, we get:
x = 1 or x = 400

Since the breadth cannot be negative, we discard the solution x = 400.

So, we take x = 1, which gives us b^2 = 1.
Therefore, b = 1 cm.

Substituting the value of b in equation 2, we get:
l = 20/1 = 20 cm

Calculating the perimeter of the rectangle:

The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + breadth)

Substituting the values of length (l) and breadth (b), we get:
Perimeter = 2 * (20 + 1) = 2 * 21 = 42 cm

Therefore, the correct answer is option (B) 18 cm.

Answer is b