1. **State the problem:** We have two similar triangles TUV and WXY. We know side lengths VU = 2, VT = 3, and YX = 12.6. We need to find the length of side YW. 2. **Recall the property of similar triangles:** Corresponding sides of similar triangles are proportional. This means: $$\frac{VU}{YX} = \frac{VT}{YW}$$ 3. **Set up the proportion:** Using the given sides, $$\frac{2}{12.6} = \frac{3}{YW}$$ 4. **Solve for $YW$:** Cross-multiply: $$2 \times YW = 3 \times 12.6$$ $$2 \times YW = 37.8$$ Divide both sides by 2: $$\cancel{2} \times YW = \frac{37.8}{\cancel{2}}$$ $$YW = 18.9$$ 5. **Answer:** The length of side $YW$ is $18.9$ units.