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Finding Square Using the 3-4-5 Rule

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Long before modern times, a Greek mathematician named Pythagoras was credited with discovering and proving what would hence be called the Pythagorean Theorem. While it is still called a theorem, it may have more proofs than any other in Euclidean Geometry. And although it has been credited to Pythagoras, it was likely used for thousands of years before being proven by the Greek mathematician.

Does this mean that, for the remainder of this article, I'm going to be expecting you to perform complicated math? Quite the opposite actually. I don't even expect you to know the old "a-squared plus b-squared equals c-squared" axiom. Instead, we're going to use a simple little trick, called the 3-4-5 rule.

I would be surprised if there is a carpenter or home-builder alive today that hasn't used the 3-4-5 rule, because is is extremely simple, even though it is actually using the Pythagorean Theorem.

The rule is this:

On one side of a corner, measure three inches from the corner and make a mark. On the opposite side of the corner, measure four inches from the corner and make a mark. Next, measure between the two marks. If the distance is five inches, your corner is square!


How does this work? By using the Pythagorean Theorem. If we plug the following values into the theorem (a=3, b=4, c=5), we find that the equation is true: three-squared (9) plus four-squared (16) is equal to five-squared (25).

The beauty of this rule is that it is scalable. In other words, if you were laying out the foundation of your new home, you would have strings stretching between batter boards. You wouldn't be accurate enough using the 3-4-5 rule in inches, but you'd be pretty close to spot-on measuring in feet, with the first side of 3-feet, the second side of 4-feet and the measurement between the two marks (the hypotenuse) of 5-feet.

If you'd prefer metric, you could use 300mm and 400mm for the two sides and 500mm for the hypotenuse. You could move up to yards, meters or miles; it doesn't really matter what scale you use as long as you maintain the standard relationship of 3-4-5.
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