This is the traditional "Farmer Problem" in which the farmer is trying to enclose a rectangular pasture using a fixed amount of fencing on three sides, but using a barn or a river as the fourth side (so no fencing needed there). One might think of this problem in a differential calculus class, but the way I have it written even middle school students can back into the ideas.
This problem has many layers of questioning to help the kids think. Your students will talk talk talk to each other as they try to appease this Fickle Farmer! This is a great problem for middle school, algebra one, algebra 2. precalculus, and even calculus. I would even use it for in-service and pre-service teachers.
I have written it so that no calculator is needed.