1. **State the problem:** We have triangle SWU with side SW = 45. Inside it, segment UV is parallel to SW and proportional. Given segments WV = 16 and TV = 15, we need to find the length UV. 2. **Identify the proportionality rule:** When a segment inside a triangle is parallel to one side, it creates similar triangles. The sides are proportional. The formula is: $$\frac{UV}{SW} = \frac{TV}{TW}$$ where TW = TV + WV. 3. **Calculate TW:** $$TW = TV + WV = 15 + 16 = 31$$ 4. **Set up the proportion:** $$\frac{UV}{45} = \frac{15}{31}$$ 5. **Solve for UV:** Multiply both sides by 45: $$UV = 45 \times \frac{15}{31}$$ 6. **Simplify the expression:** $$UV = \frac{45 \times 15}{31} = \frac{675}{31}$$ 7. **Final answer:** $$UV = \frac{675}{31} \approx 21.77$$ So, the missing length UV is approximately 21.77 units.