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?