Henry Ernest Dudeney/Puzzles and Curious Problems/222 - Folding a Pentagon/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $222$

Given a ribbon of paper, as in the diagram, of any length -- say more than $4$ times as long as broad --

it can all be folded into a perfect pentagon,

with every part lying within the boundaries of the figure.

The only condition is that the angle $ABC$ must be the correct angle of two contiguous sides of a regular pentagon.

How are you to fold it?

By folding $A$ over, find $C$, so that $BC = AB$.

Then fold as in Figure $1$ across the point $A$.

This will give point $D$.

Fold as in Figure $2$, making the edge of the ribbon lie along $AB$.

This will give point $E$.

Continue the fold as in Figure $3$, and so on, until all the ribbon lies in the pentagon.