Most builders know a simple geometry trick that makes it dirt simple to lay out a square corner for your patio, deck or other structure. All you need is a couple of tape measures. It’s all because of the Pythagorean Theorem and the 3-4-5 right triangle.
Skip the Explanation and go straight to the How to ==>
If you happened to sleep through class that day (or ditched school instead) you may not remember who Pythagoras was or what his “theorem” means to you. So let me refresh that vague memory.
The Pythagorean Theorem says that the sum of the squares on the sides of a right triangle are equal to the square of the hypotenuse.
So what? Well, that little bit of information has been put to use by builders and surveyors for centuries to lay out square corners. Here’s why: a “right triangle” is one that has a 90° or square corner, which is the gold standard for building. The hypotenuse is the long side, the one opposite the 90° corner. Old Pythagoras deduced that if you square the lengths of the two short sides and add the numbers together, the sum will be equal to the square of the length of the third side.
If you have a right triangle whose sides are 5” and 6”, you can figure out the length of the long side: 5 x 5 = 25, 6 x 6 = 36, and the sum is 61. The long side is 7.81025” long. The square root of 61 (according to my calculator
short sides of a triangle are 3” and 4” long. The squares are 3 x 3 = 9 and 4 x 4 = 16, so the long side has a length that is the square root of 25 – and that’s a simple “5.” Some builder figured out that they could use this relationship, commonly called a 3-4-5 right triangle, to lay their square corners. One interesting feature of a 3-4-5 triangle is that you can multiply the three numbers by any constant and the same relationship holds true, so the 6-8-10 and 9-12-15 triangles are also right triangles.
What all that means is that you can use this ancient relationship to define a square corner for any project that’s too big for a framing square.
And here’s how you do it:
What You’ll Need
• Three stakes
• Two tape measures
How to Lay Out a Square Corner
1) Define one corner and drive a stake at that point. This is Stake A.
2) Use one of your tape measures to measure exactly eight feet along one side of your structure. Drive a second stake at the eight-foot point. This is Stake B.
3) Hook tape measure #1 onto Stake A and tape measure #2 onto Stake B.
4) Extend tape measure #1 a bit more than six feet.
5) Extend tape measure #2 a bit more than ten feet.
6) Swing the two tapes back and forth until the six foot mark on #1 and the ten foot mark on #2 are touching. Have your helper drive Stake C at this point.
7) String lines connecting the two pair of stakes (A-B and A-C)
The line that connects Stakes A and C now forms a right angle with the line that connects Stakes A and B. It’s as simple as that!