1. **Problem statement:** Given triangle $PRS$ with $QT$ as the midsegment parallel to side $RS$, and $QT = 19$, find the length of $RS$. 2. **Formula and rule:** The midsegment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and its length is half the length of that side. 3. **Apply the theorem:** Since $QT$ is the midsegment parallel to $RS$, we have: $$QT = \frac{1}{2} RS$$ 4. **Substitute the given value:** $$19 = \frac{1}{2} RS$$ 5. **Solve for $RS$:** Multiply both sides by 2: $$RS = 2 \times 19 = 38$$ 6. **Answer:** The length of side $RS$ is $38$ units.