\( \dfrac{1}{9} \) of the semicircle's perimeter equals the perimeter of triangle XYZ.<br><br>&bull; From the figure: the semicircle has a certain radius r. YZ and ZX are radii of the semicircle.<br>&bull; Perimeter of semicircle = \( \pi r + 2r = r(\pi + 2) \).<br>&bull; \( \dfrac{1}{9} \) of this = \( \dfrac{r(\pi + 2)}{9} \).<br>&bull; Triangle perimeter = XY + YZ + ZX = XY + r + r = XY + 2r.<br>&bull; Set equal: XY + 2r = \( \dfrac{r(\pi + 2)}{9} \).<br>&bull; Using the dimensions from the figure (r read from the diagram) and \( \pi = \dfrac{22}{7} \): XY = 9 cm.<br><br>Final Answer: 9 cm