If you fold a rectangular piece of paper in half

Question

If you fold a rectangular piece of paper in half and the resulting rectangles have the same aspect ratio as the original rectangle, then what is the aspect ratio of the rectangles?

What's the solution needing verification? – Jean-Sébastien May 19 '15 at 18:34 — Jean-Sébastien, May 19 '15 at 18:34
Agreed. This is a duplicate. – Sean Henderson May 19 '15 at 18:43 — Sean Henderson, May 19 '15 at 18:43

score 1 · Answer 1 · answered May 19 '15 at 18:37

1

$$ \frac{\text{width}}{\text{lengh}}=\sqrt{2} $$

Have a look here

answered May 19 '15 at 18:37

ParaH2

1,682

score 0 · Answer 2 · answered May 19 '15 at 18:42

Assume the original rectangle is $x$ wide and $a \cdot x$ long, where a is the requested aspect ratio. If we fold the paper in half (lengthwise), the resulting rectangles will be $\frac{a \cdot x}{2}$ wide and $x$ long. Equating these ratios, we find that

$$a = \frac{1}{a / 2} = \frac{2}{a}$$

Solving this simple equation yields

$$a=\sqrt{2}$$

If you fold a rectangular piece of paper in half

2 Answers2