The Problem of the Month
These problems are my attempt to give high school students, like you, a glimpse into "real mathematics" by creating a math puzzle which will challenge you to think in ways that you have never thought before. Typically, in your high school math classes, you are given a problem to solve and a fixed step-by-step procedure for solving that type of problem — follow the steps, and you are certain to get an answer. However, "real mathematics" is not like that. When mathematicians work on problems, they often start off with no idea about how to solve the problem. There are lots of math questions that no one yet knows how to solve. I invite you to stretch your mind and take my mathematics challenge. I look forward to see what you come up with.
— Joseph DiMuro, Associate Professor for the Department of Math and Computer Science
The Fourth Corner
Here we have a picture of a rectangle: I’ve labeled the corners A, B, C, and D, in clockwise order. I’ve also marked a fifth point E (not on the rectangle), and I’ve given the distances from E to three of the four corners: AE=5, BE=10, and DE=11. Your task for this month is to find the fourth distance, CE.
By the way: this diagram is not to scale, so you can’t find the fourth distance simply by measuring.
Send your answers to firstname.lastname@example.org by September 30, 2017.