The area of a square is 1156 cm² . What is the respective ratio between the length and the breadth of a rectangle whose length is twice the side of the square and whose breadth is 14 cm less than the side of the square?

17 : 5

We have,

Area of a square = 1156 cm²

Area of Square = Side²

Length of rectangle = twice the side of the square

Breadth of rectangle = Side of square - 14 cm

Side of square = \(\sqrt {1156}\) = 34 cm

Now,

Length of rectangle = 2 × 34 = 68 cm

Breadth of rectangle = 34 - 14 = 20 cm

Ratio = 68 : 20 = 17 : 5