1. **State the problem:** We are given a rectangle BCDE with side BC labeled as $4t - 17$ and side DE labeled as $6t - 29$. We need to find the length of side DE. 2. **Recall properties of rectangles:** In a rectangle, opposite sides are equal in length. Therefore, side BC equals side DE. 3. **Set up the equation:** Since BC = DE, we have: $$4t - 17 = 6t - 29$$ 4. **Solve for $t$:** Subtract $4t$ from both sides: $$\cancel{4t} - 17 = 6t - \cancel{4t} - 29 \implies -17 = 2t - 29$$ Add 29 to both sides: $$-17 + 29 = 2t - 29 + 29 \implies 12 = 2t$$ Divide both sides by 2: $$\frac{12}{\cancel{2}} = \frac{2t}{\cancel{2}} \implies 6 = t$$ 5. **Find DE:** Substitute $t=6$ into $DE = 6t - 29$: $$DE = 6(6) - 29 = 36 - 29 = 7$$ **Final answer:** $$\boxed{7}$$