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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A Simpler Solution

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

Last week, I emailed you a way to solve a simple math puzzle – how do you find a rectangle whose area equals its perimeter?

I took the puzzle, mixed in a little bit of algebra, and voila! A puzzle solution factory popped out, letting you generate rectangles from pythagorean triplets.

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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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Perimeter, Area and Volume

How long and wide must a rectangle be, for its area to equal its perimeter? Assume the width and length are whole numbers.

This is a nice little puzzle to let younger kids explore – if they find the puzzle as interesting or frustrating as I expect, they’ll remember the formulae for perimeter and area for the rest of their lives. For older kids, a bit of algebra gives the answer quickly.

Continue reading Perimeter, Area and Volume