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Rectangle to Square (Posted on 2013-08-13) Difficulty: 2 of 5

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    
No Rating
Solution: (Hide)

Ady's link shows how to construct a line segment
having length s such that s2 = |AB||BC|.

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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(3): Full solutionDaniel2013-08-16 14:50:13
re(2): Full solutionBractals2013-08-16 13:47:57
re: Full solutionDaniel2013-08-16 10:34:57
re(2): Full solutionJer2013-08-15 18:05:40
re: Full solutionDaniel2013-08-15 17:10:36
SolutionFull solutionJer2013-08-15 13:12:13
re: full solution - spoiler; not reallyLarry2013-08-14 08:28:45
Solutionfull solution - spoilerAdy TZIDON2013-08-14 02:00:45
SolutionOne wayJer2013-08-13 14:47:52
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