1. **State the problem:** We are given a triangle $\triangle STV$ with a midsegment $RU$. The length of side $ST$ is $z$, and the length of the midsegment $RU$ is $z - 11$. We need to find the value of $z$. 2. **Recall the midsegment theorem:** The midsegment of a triangle is parallel to one side and its length is half the length of that side. In this case, since $RU$ is a midsegment parallel to $ST$, we have: $$RU = \frac{1}{2} ST$$ 3. **Set up the equation:** Substitute the given lengths: $$z - 11 = \frac{1}{2} z$$ 4. **Solve for $z$:** Multiply both sides by 2 to eliminate the fraction: $$2(z - 11) = z$$ Simplify the left side: $$2z - 22 = z$$ Subtract $z$ from both sides: $$2z - z - 22 = 0 \implies z - 22 = 0$$ Add 22 to both sides: $$z = 22$$ 5. **Conclusion:** The value of $z$ is $22$.