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?