1. **State the problem:** We have a rectangular garden with an area of 40 m². The length and width are whole numbers, and we want to find the smallest possible perimeter. 2. **Formula used:** - Area of rectangle: $$A = l \times w$$ where $l$ is length and $w$ is width. - Perimeter of rectangle: $$P = 2(l + w)$$ 3. **Important rules:** - Both $l$ and $w$ must be whole numbers. - Their product must be 40. - We want to minimize $P = 2(l + w)$. 4. **Find all factor pairs of 40:** - $(1, 40)$ - $(2, 20)$ - $(4, 10)$ - $(5, 8)$ 5. **Calculate perimeter for each pair:** - For $(1, 40)$: $$P = 2(1 + 40) = 2 \times 41 = 82$$ - For $(2, 20)$: $$P = 2(2 + 20) = 2 \times 22 = 44$$ - For $(4, 10)$: $$P = 2(4 + 10) = 2 \times 14 = 28$$ - For $(5, 8)$: $$P = 2(5 + 8) = 2 \times 13 = 26$$ 6. **Conclusion:** The smallest perimeter is $$26$$ meters, achieved when the sides are 5 m and 8 m. **Final answer:** The smallest possible perimeter is $26$ meters.