All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
A Square Triangulation (Posted on 2005-01-31) Difficulty: 3 of 5
Is it possible to cut a square into seven isosceles right triangles, no two of which are congruent?

See The Solution Submitted by David Shin    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution (spoilers) | Comment 2 of 4 |

Yes, it is possible.

Draw a square 5sqrt2 units on each side.  I labeled mine ABCD starting with the upper left corner and going clockwise.

Draw the diagonal AC.  Draw point E on DC such that DE = 2sqrt2 units long and EC = 3sqrt2 units long.  Draw point F on AC such that EF is perpendicular to DC.  EF is 3sqrt2 units long.

Draw point G on AD such that AFG is a right triangle with <F = 90 degrees.

Draw point H on FG such that FHE is a right triangle with <H = 90 degrees.

Draw point I on HE such that DIE is a right triangle with <I = 90 degrees.  Draw GI.

Triangles in descending order of size:

ABC: AB=BC=5sqrt2. AC=10.

CEF: CE=EF=3sqrt2. CF=6.

AFG: AF=FG=4. AG=4sqrt2.

EHF: EH=HF=3. EF=3sqrt2.

DIE: DI=IE=2. DE=2sqrt2.

DGI: DG=GI=sqrt2. DI=2.

GHI: GH=HI=1. GI=sqrt2.


changed strange boxes and a's with squigly lines to 'sqrt'.

Edited on February 1, 2005, 2:15 am
  Posted by Dustin on 2005-02-01 02:13:25

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information