Henry Ernest Dudeney/Puzzles and Curious Problems/201 - Square and Triangle/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $201$

Take a perfectly square piece of paper,

and fold it as to form the largest possible equilateral triangle.

A triangle in which the sides are the same length as those of the square, as shown in our diagram,

will not be the largest possible.

Of course, no markings or measurements may be made except by the creases themselves.

Fold the square in half to get the crease $EF$.

Fold along $AH$ to get $B$ to lie on $EF$ at $G$.

With that fold in place, fold $HGJ$.

While $B$ is on $G$, fold $AB$ back on $AH$ to get the line $AK$.

You can now fold the triangle $AJK$, which is the largest possible equilateral triangle that can be obtained.