23. A pyramid is intersected by a plane parallel to the base, so that its lateral surface is divided into two parts of equal area. In what ratio does this plane divide the lateral edges of the pyramid?
23. When intersecting a pyramid with a plane parallel to the base, we obtain a pyramid similar to the given one with the center at the vertex of the pyramid. The areas of similar polygons are proportional to the squares of the corresponding sides. In this case, the latter ratio is equal to the ratio of the squares of the heights of the original and similar pyramids, i.e., if the distance from the section plane to the vertex is $x$, and the height of the original pyramid is $h$, then $\frac{S^{\prime}}{S}=\frac{x^{2}}{h^{2}}$. This ratio equals $\frac{1}{2}$ if $x^{2}=\frac{h^{2}}{2}$, i.e., $x=\frac{h}{\sqrt{2}}$. (We can say that the distance $x$ is the length of the side of a square with a diagonal of length $h$.)