# Equidecomposition of Two Rectangles

What is it about?

A Mathematical Droodle

What if applet does not run? |

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Copyright © 1996-2018 Alexander Bogomolny

What if applet does not run? |

A rectangle is equidecomposable with a square of equal area. It follows that two rectangles of equal area are equidecomposable. The applet illustrates a little different and probably more economical way to prove this fact. Each of the two rectangles can be split into two equal triangles and a parallelogram. In fact, all four triangles are equal, whereas the parallelograms have a common base and the height. These, as we know, are equidecomposable.

Assume the triangles have sides a, b and c, d, so that

### References

- T. Andreescu, B. Enescu,
*Mathematical Olympiad Treasures*, Birkhäuser, 2004

### Equidecomposition by Dissiection

- Carpet With a Hole
- Equidecomposition of a Rectangle and a Square
- Equidecomposition of Two Parallelograms
- Equidecomposition of Two Rectangles
- Equidecomposition of a Triangle and a Rectangle
- Equidecomposition of a Triangle and a Rectangle II
- Two Symmetric Triangles Are Directly Equidecomposable
- Wallace-Bolyai-Gerwien Theorem
- Perigal's Proof of the Pythagorean Theorem
- A Proof Perigal and All Others After Him Missed
- Dissection of a Vase
- Curvy Dissection

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Copyright © 1996-2018 Alexander Bogomolny65620403