1. **State the problem:** We have triangle VTU with WX parallel to TU. Given lengths are $VU=7.2$, $WV=5$, and $TW=4$. We need to find the length of $VX$. 2. **Use the properties of parallel lines in triangles:** When a segment (WX) is drawn parallel to one side (TU) of a triangle (VTU), it creates similar triangles VWX and VTU. 3. **Set up the similarity ratios:** Since $WX \parallel TU$, triangles $VWX$ and $VTU$ are similar, so corresponding sides are proportional: $$\frac{VW}{VT} = \frac{VX}{VU} = \frac{WX}{TU}$$ 4. **Find $VT$:** Since $W$ lies on $VT$, and $VW=5$, $TW=4$, then $$VT = VW + WT = 5 + 4 = 9$$ 5. **Use the ratio to find $VX$:** Using the ratio $$\frac{VW}{VT} = \frac{VX}{VU}$$ Substitute known values: $$\frac{5}{9} = \frac{VX}{7.2}$$ 6. **Solve for $VX$:** Multiply both sides by 7.2: $$VX = \frac{5}{9} \times 7.2$$ 7. **Simplify:** $$VX = \frac{5}{\cancel{9}} \times \frac{\cancel{7.2}}{1} = 5 \times 0.8 = 4$$ **Final answer:** $$VX = 4$$