What is the ratio between the area of a square and the area of the square constructed on its diagonal?

Explanation

If the side of the original square is 's', its area is s². The diagonal measures s√2, so the square built on the diagonal has an area of (s√2)² = 2s². Therefore, the ratio of the original square's area to the new square's area is s² : 2s², which simplifies to 1 : 2.