The ratio of the area of a square to that of the square drawn on its diagonal is

Correct option is B

Given:

Let the side length of the square be s.

Explanation:

The area of the square is:

​$$\text{Area of square} = s^2$$​​

The diagonal of the square is:

​$$d = \sqrt{s^2 + s^2} = s\sqrt{2}$$​​

The area of the square drawn on the diagonal is:

​$$\text{Area of square on diagonal} = d^2 = (s\sqrt{2})^2 = 2s^2$$​​

Now, the ratio of the area of the original square to the area of the square drawn on its diagonal is:

​$$\frac{\text{Area of square}}{\text{Area of square on diagonal}} = \frac{s^2}{2s^2} = \frac{1}{2}$$​​

Thus, the ratio of the areas is:

1 : 2