Alright i this idea originally came up while i was do a related rates problem for homework in calc class. so the problem was to find how fast the area of a rectangle was increasing, given the rate of change of one of the sides, and the fact that the proportions of the triangle will never change. i understand how to get the answer and know that it is pretty simple.
My question: is there any known way of relating the rate of change of the diagonal of the rectangle, to the rate of change of the area of the rectangle as a whole.
my idea is that if you have the rate of change of the diagonal you can relate it to the rate of change of the triangle and then to the rectangle as a whole.
or i might just be crazy.