1. **Problem statement:** Given parallelogram RSTU, find the length of diagonal SU. 2. **Key property:** In a parallelogram, the diagonals bisect each other. This means the point V, where diagonals intersect, divides SU into two equal segments SV and VU. 3. **Given:** - Length of SV = $2x + 3$ - Length of VU = $4x - 17$ 4. **Since SV = VU$, set the expressions equal:** $$2x + 3 = 4x - 17$$ 5. **Solve for $x$:** $$2x + 3 = 4x - 17$$ $$3 + 17 = 4x - 2x$$ $$20 = 2x$$ $$x = \frac{20}{2}$$ $$x = 10$$ 6. **Find the length of SV (or VU) by substituting $x=10$:** $$SV = 2(10) + 3 = 20 + 3 = 23$$ 7. **Since SU = SV + VU and SV = VU, then:** $$SU = 2 \times SV = 2 \times 23 = 46$$ **Final answer:** The length of diagonal SU is $46$ units.