1. **Problem:** Find the perimeter of the house in terms of $c$. 2. **Formula:** The perimeter of a polygon is the sum of the lengths of all its sides. 3. **House sides:** $4c + 2$, $4c + 1$, $3c - 2$, and $2c$. 4. **Calculate perimeter:** $$P_{house} = (4c + 2) + (4c + 1) + (3c - 2) + 2c$$ 5. **Simplify:** $$P_{house} = 4c + 2 + 4c + 1 + 3c - 2 + 2c = (4c + 4c + 3c + 2c) + (2 + 1 - 2) = 13c + 1$$ 6. **If $c = 5$:** $$P_{house} = 13(5) + 1 = 65 + 1 = 66$$ --- 7. **Problem:** Find the perimeter of the garage in terms of $d$. 8. **Garage sides:** $3d - 2$ and $5d + 1$ (rectangle, so opposite sides equal). 9. **Calculate perimeter:** $$P_{garage} = 2(3d - 2) + 2(5d + 1) = 2(3d - 2 + 5d + 1) = 2(8d - 1) = 16d - 2$$ 10. **If $d = 3$:** $$P_{garage} = 16(3) - 2 = 48 - 2 = 46$$ **Final answers:** - House perimeter in terms of $c$: $13c + 1$ - House perimeter when $c=5$: $66$ - Garage perimeter in terms of $d$: $16d - 2$ - Garage perimeter when $d=3$: $46$