The discussion revolves around determining the dimensions of a white rectangle within a tile, defined by segments with one and two tick marks, represented as lengths $a$ and $b$. The relationship between these lengths is established with the equation $a^2 + b^2 = 50$. Using the Pythagorean theorem, the diagonal length of the rectangle, denoted as $\overline{MK}$, is calculated as $\sqrt{2(a^2 + b^2)}$. Substituting the known value, the final length of $\overline{MK}$ is determined to be 10 cm. The conversation effectively concludes with the confirmation of this diagonal length.