1. **Problem Statement:** Given two congruent polygons JIHG and UVWX, find the length of side UV. 2. **Understanding Congruence:** Congruent polygons have corresponding sides and angles equal. Since JIHG \cong UVWX, side UV corresponds to side JI. 3. **Identify Corresponding Sides:** The order of vertices indicates correspondence: J \leftrightarrow U, I \leftrightarrow V, H \leftrightarrow W, G \leftrightarrow X. 4. **Given Lengths:** Side JI has length 48 mm. 5. **Conclusion:** Since UV corresponds to JI and the polygons are congruent, length of UV = length of JI = 48 mm. **Final answer:** $$\boxed{48\text{ mm}}$$