A square has an area of 4096 square centimeters. If a rectangle's length is twice the side length of this square and its breadth is 24 cm shorter than the square's side, what is the ratio of the rectangle's breadth to its length?

Explanation

Let the side of the square be 'a' cm. Since the area is 4096 cm², a² = 4096, so a = 64 cm. The rectangle's length is twice the side, so length = 2a = 128 cm. The breadth is 24 cm less than the side, so breadth = a - 24 = 40 cm. Therefore, the ratio of breadth to length is 40 : 128, which simplifies to 5 : 16. Since this ratio is not among the given options, the correct choice is 'None of the above'.