So, I’d like to believe that most people know the Pythagorean Theorem. The famous a^{2} + b^{2} = c^{2} theorem that relates the lengths of the sides of a right triangle.

Earlier this month, I was helping my mom move. The moving company requested to know the size of my mom’s televisions. Since my mom has a 1990s console-style Cathode-ray tube (CRT) television, I was going to measure the length, width, depth, and screen size so that the company would have an accurate idea of the size of the television as possible.

If you didn’t know, the screen size of a TV is always measured diagonally, which is a practice that was started by early TV manufacturers simply to make the size of the TV more impressive. Mathematically, the diagonal of a TV will always be longer than its length or width.

Another thing to note is that for old CRT TVs like my mom’s, the size of the TV’s diagonal measurement is from the outside edges of the casing. So, the console would be included as part of the measurement. However, for newer LCD TVs, the size of the TV’s diagonal only consists of the view-able screen.

With all of this being said, my friend Matt made a comment to me that I didn’t need to measure the screen size of my mom’s TV if I already knew the length and width. He suggested that I just save myself the time of taking the extra measurement and the trouble of trying to remember it and simply use the Pythagorean Theorem to find the screen size later.

And there you have it – a real-life application of the Pythagorean Theorem that saved me not only time but also the frustration of trying to remember an extra measurement.

I’ve been thinking about how I could frame this problem in a way to use it with my students and came up with the following:

Suppose you are helping a family member move an old TV from their home. You are on the phone with the moving company, and they want to know the size (diagonal) of the television. Your family member only told you that the TV is 25 in by 23 in, but did not tell you the length of the diagonal. You don’t have time to get the measurement of the diagonal because the company is having a 50% sale on moving costs that ends at the end of the day. So, you must tell them the size of the television before you hang up the phone. What are you going to tell them is the size of the TV?

Anyway, I hope you enjoyed this look at a real-life application of the Pythagorean Theorem and consider using it or a similar problem in your classroom.