1. **Problem Statement:** Find the length AB of rhombus FGHI given the side length expressions. 2. **Recall Properties of a Rhombus:** All sides are equal in length. 3. **Given:** Segment GH = $3x + 1$, Segment HJ = $x + 9$. 4. Since FGHI is a rhombus, $GH = HJ$. 5. Set up the equation: $$3x + 1 = x + 9$$ 6. Solve for $x$: $$3x + 1 = x + 9$$ $$3x - \cancel{x} + 1 = \cancel{x} + 9$$ $$2x + 1 = 9$$ $$2x = 9 - 1$$ $$2x = 8$$ $$x = \frac{8}{2}$$ $$x = 4$$ 7. Find the length AB (which equals GH or HJ): $$AB = 3x + 1 = 3(4) + 1 = 12 + 1 = 13$$ **Final answer:** The length AB is 13 units.