1. **State the problem:** We have a swimming pool with an inside perimeter of 24 m and an outside perimeter of 48 m. We want to find how many stepping stones are needed to cover the outside area around the pool, given that 6 stepping stones cover 1 square meter. 2. **Identify the shape and formulas:** Assuming the pool and the outside area are rectangular for simplicity, the perimeter $P$ of a rectangle is given by: $$P = 2(l + w)$$ where $l$ is length and $w$ is width. 3. **Find dimensions of the inside pool:** Given inside perimeter $P_i = 24$ m, $$24 = 2(l + w) \implies l + w = 12$$ 4. **Find dimensions of the outside area:** Given outside perimeter $P_o = 48$ m, $$48 = 2(L + W) \implies L + W = 24$$ where $L$ and $W$ are the length and width of the outside area. 5. **Relate inside and outside dimensions:** The outside area surrounds the pool, so the difference in length and width is twice the border width $x$: $$L = l + 2x$$ $$W = w + 2x$$ 6. **Use the sums:** $$L + W = (l + 2x) + (w + 2x) = (l + w) + 4x = 12 + 4x$$ Given $L + W = 24$, so: $$12 + 4x = 24 \implies 4x = 12 \implies x = 3$$ 7. **Calculate areas:** Inside area: $$A_i = l \times w$$ Outside area: $$A_o = L \times W = (l + 2x)(w + 2x)$$ 8. **Express $w$ in terms of $l$:** From step 3, $w = 12 - l$ 9. **Calculate inside area:** $$A_i = l(12 - l) = 12l - l^2$$ 10. **Calculate outside area:** $$A_o = (l + 6)(12 - l + 6) = (l + 6)(18 - l) = 18l - l^2 + 108 - 6l = 12l - l^2 + 108$$ 11. **Calculate outside border area:** $$A_{border} = A_o - A_i = (12l - l^2 + 108) - (12l - l^2) = 108$$ 12. **Calculate number of stepping stones:** Each square meter requires 6 stepping stones, so: $$\text{stones} = 108 \times 6 = 648$$ **Final answer:** We need 648 stepping stones to cover the outside area of the swimming pool.