You Won’t Believe This Amazing Formula

[This is a back-issue of one of this site’s newsletters]

If you’ve been reading for a while, you might remember this puzzle: Can you find a rectangle whose area equals its perimeter?

For example, a 6 x 3 rectangle has a perimeter of 18 units, and the area is 18 square units. The same number!

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Rectangles and Right Triangles

Can you find a rectangle whose perimeter equals its area?

I’ll explain one way to solve this puzzle below.

Allergy warning: this product contains algebra. May contain traces of number theory.

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Pythagoras Jigsaw Puzzles

“Everyone” knows that 3×3 + 4×4 = 5×5. This little factoid, and other Pythagorean triplets, can be the basis of a nice set of puzzles. Here’s the first. If you draw a 5×5 square on graph paper, how can you cut it up (following the lines on the graph paper) so that the pieces can be rearranged to form a 3×3 square and a 4×4 square?

This is not so hard to do. Here’s one possible solution :

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