Just a warning, this is a nerdy post, but a favorite because of: **math**. If anyone needs a good practical application of math in real life for doubting teenagers just use this example because it’s the most useful example I was ever taught. Geek is the new chic so I’ve got that going for me, right?

So, in my previous post I showed * how we prepared the area *around the depot for the picket fence, created the steps.

But how did we create a perfect rectangle with all right angles?

**The Pythagorean Theorem**

This is a super simple method that requires only 2 measuring tapes and a few marking stakes.

Here are the basic steps:

**Step 1:** First you need one side of the square or rectangle to start with. I measured off of the train depot to get my first side:

**Step 2:** I used string line to mark the line and wrote down what the final measurement was (21 feet):

Here is what step 1 and 2 looked like in real life:

**Step 3:** We attached a measuring tape to one of the stakes from the line (A) just created and pulled in the direction for side B. You’ll leave the measuring tape stretched out, not sure of the straight line yet, until you attach a second measuring tape:

**Step 4:** I estimated the length of side B to be 49 feet at this point.

Here is what step 3 and 4 looked like in real life:

**Step 5:** I attached another tape measure on the other side of A to form line C. Basically I have one tape measure for line B and one tape measure for line C. To figure out what the exact measurement of line C needs to be in order to create a right angle I use the Pythagorean Theorem. (if you don’t remember it I’m going to remind you)

Here are the basic calculations if you need to follow them step-by-step, but basically you are just solving for c to get your diagonal measurement:

The good news is you can use a calculator or your smart phone to do all this math…but you have to turn it landscape in the calculator function to her the square root to show up:

Note: I’m only sharing this because I was like:THERE’S NO SQUARE ROOT ON MY PHONE!and then Brett turned it to LANDSCAPE for me and solved the entire crisis. And then I was like: it’s 53 and 3 inches and he had to correct me on that too. He’s so smart.

So anyway back to the triangle…line C will have to be 53.3 feet in order to form a perfect right angle where line A and B meet:

**Step 6:** Pull both measuring tapes tight and adjust them until they intersect at 49 feet on measuring tape B and 53.3 feet on measuring tape C:

Step 6 in real life:

Once we have our right triangle, we know that we have a perfect “L” shaped corner to start at. Make sure to mark the spot where the measuring tapes intersect with a stake so you don’t lose it:

Repeat the process for the other side of the fence (you already have all the measurements you need) and you will have all right angles. Use smaller triangles if needed to work around stationary objects. Next time we’ll start the actually digging and building of the fence!

The Old Depot Project is sponsored by **Lowe’s Home Improvement**. A huge thank you to them!

karen608 says

Oh sweet! A male friend of mine talks about this but I always forget. Now you state it clearly, thank you!!!

SusanIrene says

Thanks so much for the landscape square root tip. I hadn’t found that on my new phone yet. I just found my old slide rules from math classes last century and gave up trying to remember how to use them…..phone much easier.

Great illustrations. I’m going to show them to my grandboys to show how important math is (which they like, by the way).

fjnorm says

Love this!! I am a math teacher and we used to do problems like this in my class! When asked “When am I ever going to use this?” I would tell my teens all the time they could use the Pythagorean Theorem to make sure building were square and they always responded that they would just hire someone else to do that part… to which I would tell them that THAT PERSON would have to know the math and this is where you learn it!