Or you could also consider right?
Let be an acute triangle. Let and be inscribed rectangles in . Also, let be the area of a polygon . Does have a maximum? If so, what is it? and range over all rectangles and ranges over all triangles.
So they probably gave as an acute triangle for some reason. I am not sure why we need both and , since they are both rectangles. If you just let range over all rectangles, wouldn't that "cover" ? (e.g. we could instead consider )? Now is the area of all the triangles inside right?
Any ideas? Use any derivative tests?
Yes, the [A(R) +A(S)] / A(T) has a maximum.
The A(T) is constant.
The A(R) and/or A(S) are variable, depending on how they are positioned inside the triangle.
If the positions of A(R) +A(S) is maximized, then the [A(R) +A(S)] /A(T) is maximized also.