The solution of
how to fold it the equilateral triangle.

figure htfi.1 
Fold the square in to half from vertical side and half again twice from horizontal

figure htfi.2 
then open the paper to half you can see three lines of cut marks on the paper as shown.
Then take the bottom one to the second fold and get the 3rd part split in to half.

figure htfi.3 
Consider the 2nd part as the two third of the height of triangle and top half of thrid part as the one third of height of triangle. The red line in the figure htfi.3 as the base of the triangle. Then from the center connect the base by folding the upper part of height of triangle as shown.

figure htfi.4 




Move point P in the figure around point O such that it touches the base line of triangle and then we have found our other two vertexes of triangle.

figure htfi.5 
Fold the paper along the line which joins the newly found vertex Q and the center O.
Then cut straight along the base line(in the figure along PQ) and you have produced the equilateral triangle from the square.

figure htfi.6 
Now scream with joy that you have found away to cut the square paper to free the equilateral part from the dungeon.
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