Metric paper which always has the same ratio of dimensions when folded in half that being 1/sqrt(2). How was the logic behind this derived?

Question

Metric paper which always has the same ratio of dimensions when folded in half that being 1/sqrt(2). How was the logic behind this derived?

In: Mathematics

Answer 1

The long side of a piece of paper is 1 unit. The short side is X units. Fold it in half, the long side is X units, and the short side is 0.5 units.

The ratio of the sides is long / short.

So we need a value of X where 1/X = X/0.5. We can rearrange this, and see X²=½ or X=1/sqrt (2). It’s the only number that works.