242. The lengths of the edges of a rectangular parallelepiped are $a, b$, and $c$. What is the maximum value of the area of the rectangular projection of this parallelepiped onto a plane?
242. Note that the area of the projection of any parallelepiped is always twice the area of the projection of any triangle with vertices at the ends of three edges of the parallelepiped, emanating from one of its vertices. For a rectangular parallelepiped, all such triangles are equal. The largest area of the projection of a rectangular parallelepiped will be in the case when one of such triangles is parallel to the plane onto which the parallelepiped is projected. Thus, the largest area of the projection is $\sqrt{a^{2} b^{2}+b^{2} c^{2}+c^{2} a^{2}}$.