Hi, I'm a senior in calculus. I know this thread list is supposed to be for university students, but there's no calculus listed in the high school section. My tutor referred me to this site because we couldn't solve this before the session ended. The problem actually sounds like a geometry problem, and maybe that's why I'm having a hard time solving it. Anyways, on to the problem. You'll have to see the diagram to make sense of what I say here. I'm sorry, but I had to manufacture it in a paint program.
There is a rectangle (ABCD) measuring 14 x 8.5. Triangle RST is inside of the rectangle, with R between A and B, S between B and C, and T between A and D. Segments AR and RS each have variable length x. I am trying to find an expression for the length of RT in terms of x (then I am to analyze that function, but I don't anticipate any difficulties there).
So far, I've noticed that RBS and ART are right triangles no matter what x is, so I can figure out that the length of RB is 8.5-x, and use Pythagoreas' Theorem (one of the things I did manage to remember from geometry) to find that BS=x^2 - (8.5-x)^2, and that AT=RT^2 - x^2. Unfortunately, I haven't been able to go anywhere except for in circles with this information. I'm so stuck--little help, please?