I don't have much space on my desk at home, so when my monitor went kaput a few years back I had to be very careful about the size of it's replacement. Monitors are always advertised according to the length of their hypotenuse,

https://i.imgur.com/YY8YHIn.jpg

so if a monitor says it is a 22-inch monitor, it is saying it's hypotenuse is 22 inches long. This isn't very useful for me though, I need to know how wide it is to know whether it'll fit onto my desk, and to convert the hypotenuse to a width, I have to use Pythagoras.

The sides of monitors aren't often the same length though, they are usually wider than they are tall. A normal monitor (and any monitor I want to buy) will have dimensions in the ratio 16:9, i.e. for every 16 centimeters they are long horizontally, they are 9 centimeters tall vertically. In simpler terms, we can label the width of our monitor 16x and the height of it 9x, like so:

https://i.imgur.com/JxdFyLR.jpg

Image not to scale.

We know (thanks to Pythagoras) that a^2 + b^2 = c^2 , but how does this translate to our beautiful real life problem? Well it translates as (16x)^2 + (9x)^2 = (our hypotenuse)^2. (16x)^2 is 256x^2 and (9x)^2 is 81x^2 so together, c2=(81+256)x^2 or 337x^2. To get c alone we then need to square root 337x^2 , we receive 18.36x.

https://i.imgur.com/92LN2UR.jpg

Final step now. My desk only has space for a monitor 17.5 inches wide, what is the hypotenuse of said monitor (assuming it is in the ratio 16:9)? Well, if 17.5 inches = 16x, then x = (17.5/16) inches. If our hypotenuse is 18.36x, then in inches it is 18.36 times (17.5/16), (or put simply) 20.08 inches. So what size monitor am I going to buy? I'm going to buy a 20 inch monitor.

Extension Question: How tall is my monitor going to be?