\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) A rectangle with length $L$ and
width $W$ is cut into four smaller rectangles by two lines which are
parallel to the sides. Find the minimum value of the sum of the
squares of the areas of the smaller rectangles.

\medskip

\noindent b) Show that the maximum of the sums of the squares of the
areas occurs when the cutting lines correspond to sides of the
rectangle (so that there is only one rectangle).

\vfil\eject\end