Been playing with a geogebra file ( see below), the base of the triangle is fixed but as the point P moves along a horizontal line, the area does not change ( as height of the triangle is the same) but the lengths of the other two sides do, as we would expect.

I wondered how the ratio of the two sides change with the x coordinate of the point P. So in the graphics 2 window I have plotted this. I have noticed a strange looking graph that seems to have a max at 3/2 and a min at 2/3 , I can't seem to get a handle of what the function might be?

Any thoughts?