perplexus.info :: Geometry : Rectangle to Square

Rectangle to Square (Posted on 2013-08-13)

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 solution	Daniel	2013-08-16 14:50:13
re(2): Full solution	Bractals	2013-08-16 13:47:57
re: Full solution	Daniel	2013-08-16 10:34:57
re(2): Full solution	Jer	2013-08-15 18:05:40
re: Full solution	Daniel	2013-08-15 17:10:36
Full solution	Jer	2013-08-15 13:12:13
re: full solution - spoiler; not really	Larry	2013-08-14 08:28:45
full solution - spoiler	Ady TZIDON	2013-08-14 02:00:45
One way	Jer	2013-08-13 14:47:52

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info