[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!
[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.
Last week, I posted a solution to a puzzle – how can you find a rectangle whose area equals its perimeter?
This week, I’ll post a simpler solution.
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.
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.