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Rectangle to Square (Posted on 20130813) 

A rectangle ABCD is to be cut into three pieces
(with two straight line cuts) and the pieces re
arranged into a square.
Define the endpoints of the cuts.
Note 1: AB/4 ≤ BC < AB.
Note 2: A straight line cut (as the name implies)
is a cut along a straight line that
divides a piece into two pieces.

Submitted by Bractals

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Solution:

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Ady's link shows how to construct a line segment
having length s such that s^{2} = ABBC.
First cut ABCD along AE ( E on side CD such that
DE = s ).
Second cut ABCE along FG ( F on side AB such that
BF = s ) and G on side AE ( such that FG  BC ).
Slide ΔADE ( side AE along side GE until A
coincides with G ). Move ΔAFG into ΔECE.

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