On One Extremal Problem on the Euclidean Plane

Given two intersecting congruent rectangles $P_1=ABCD$ and $P_2=EFGH$ in the Euclidean plane, let $L_1$ be the length of the part of the boundary $\partial P_1$ which lies in the interior $\operatorname{int}(P_2)$ of $P_2$ and similarly let $L_2$ be the length of the part of $\partial P_2$ which lies in the interior $\operatorname{int}(P_1)$ of $P_1$. The author solves J. W. Fickett's problem of validating the inequality $\frac13 L_1\le L_2\le 3L_1$.