1. The problem states that segments AB and DE are parallel, and we have two triangles ABC and DCE with given side lengths. We need to find the length $x$ of segment CD. 2. Since AB and DE are parallel, triangles ABC and DCE are similar by the AA (Angle-Angle) similarity criterion. 3. The corresponding sides of similar triangles are proportional. Therefore, we can write the proportion: $$\frac{AB}{DE} = \frac{BC}{CE} = \frac{AC}{DC}$$ 4. From the problem, we know: - $AB = 16$ - $DE = 28$ - $BC = 22$ - $AC = 20$ - $CD = x$ 5. Using the proportion involving $AC$ and $DC$: $$\frac{AC}{DC} = \frac{AB}{DE}$$ 6. Substitute the known values: $$\frac{20}{x} = \frac{16}{28}$$ 7. Cross-multiply to solve for $x$: $$20 \times 28 = 16 \times x$$ 8. Simplify: $$560 = 16x$$ 9. Divide both sides by 16: $$\frac{\cancel{560}}{\cancel{16}} = \frac{16x}{16} \Rightarrow 35 = x$$ 10. Therefore, the length $x$ is: $$x = 35$$