A 3-4-5 Right Triangle

Image by MJ Logan

A 3-4-5 triangle is a right triangle. Side A is 3 units, side B is 4 units, and side C is 5 units. If either side A or side B is too long or too short, or the angle is not 90 degrees, the length of side C will be some other value than 5. It also works for multiples of 3-4-5 such as 9-12-15 or 12-16-20.

And here's the good part. It doesn't matter at all if the units are inches, meters, yards, miles, or any other unit you wish to make up. It works equally well for metric as for English units. Let's take a look at a practical application, the layout of a garden bed.

We'll start simply with a garden bed that is 16 feet along one edge. Put in two stakes 16-feet apart and use two tape measures. Put the hook from each tape measure on a different stake. Back out until the side is 12 feet long, and the angled tape is 20 feet long. The two stakes and the two tape measures form a triangle. Put a stake where the two tape measures meet.

Move to the other side and repeat for the fourth stake.

Your garden layout is square. That geometry you forgot just came in handy.

If you did not want one side at 12 feet, or even 16, you can still use this rule. Just make the layout for the large rectangle, then measure along the sides to make it fit. But there is a better way and all you need is a calculator.

We mentioned above that you can use multiples of 3-4-5. That works for non-integer multiples as well, all that is important is that the ratio is maintained. Divide the sides by 2 and it still works and the sides are 1.5 – 2 – 2.5.

On small projects, a framing square can keep your layout next to perfect. But once you get beyond one or two feet, you begin to introduce errors. You can check to ensure everything stayed square by using the carpenter's 3-4-5 rule.