Hey, this is Presh Talwalkar Baseball is a game of traditions and rules. Rule 2.02 two of the MLB handbook carefully defines home plate by the following geometric construction. The home base is defined as a square where one side is 17 inches. Two corners are removed. The two adjacent sides measure 8 and 1/2 inches and the remaining two sides measure 12 inches and meet at a right angle. There’s only one problem with this very carefully defined construction It’s an impossible shape mathematically. This creates an interesting geometric little puzzle. If we were to say the dimensions of 17 inches and 8 and 1/2 inches as well as the following right angles are correct, what would be the correct measure of the remaining sides? That is, can you solve for the correct value of x to make home-plate geometrically possible? Can you figure it out? Give this problem a try and when you’re ready to keep watching the video for the solution. So how can we solve for the correct value of x? Will divide the shape into two different shapes. We’ll draw a line connecting the two sides of 8 and 1/2 inches. This creates an upper rectangle and a lower isosceles right triangle. Because the upper shape is a rectangle we know that this length will be 17 inches. Now we can focus on the isosceles right triangle. By the Pythagorean theorem x squared plus x squared is equal to 17 squared. This means 2x squared is equal to 17 squared, which means x squared is equal to 17 squared divided by 2. And so x is equal to 17 divided by the square root of 2, which is approximately 12.02, which is slightly larger than the 12 inches that’s defined in the handbook. If MLB wanted to be mathematically correct, it could say in the next iteration of its handbook that the two remaining sides should measure about 12 inches. Did you figure it out? Thanks for watching this video. Please subscribe to my channel I make videos on math. You can catch me on my blog Mind Your Decisions which you can follow on Facebook, Google+ and Patreon. You can catch me on social media @preshtalwalkar, and if you like this video please check out my books. There are links in the video description.