1. **State the problem:** We are given the areas of the faces of a rectangular prism and need to find its dimensions (length, width, height). 2. **Recall the formula:** The surface area of a rectangular prism has 3 pairs of faces with areas $lw$, $lh$, and $wh$, where $l$, $w$, and $h$ are the dimensions. 3. **Identify the given areas:** The faces have areas 18, 36, and 72 square meters. 4. **Assign variables:** Let the dimensions be $l$, $w$, and $h$. Then the face areas are: $$lw = A_1, \quad lh = A_2, \quad wh = A_3$$ 5. **Match areas to given values:** The three distinct areas are 18, 36, and 72. So: $$lw = 18, \quad lh = 36, \quad wh = 72$$ 6. **Find dimensions:** From $lw=18$, express $w = \frac{18}{l}$. 7. Substitute into $wh=72$: $$w h = 72 \Rightarrow \frac{18}{l} h = 72$$ 8. Simplify: $$\frac{18}{l} h = 72 \Rightarrow 18 h = 72 l \Rightarrow h = \frac{72 l}{18} = 4 l$$ 9. Use $lh=36$: $$l h = 36 \Rightarrow l \times 4 l = 36 \Rightarrow 4 l^2 = 36$$ 10. Solve for $l$: $$l^2 = \frac{36}{4} = 9 \Rightarrow l = 3$$ 11. Find $w$ and $h$: $$w = \frac{18}{l} = \frac{18}{3} = 6$$ $$h = 4 l = 4 \times 3 = 12$$ 12. **Answer:** The dimensions are $3$, $6$, and $12$ meters. This matches the first option: 3, 6, 12.