1. **State the problem:** We are given the areas of the faces of a rectangular prism's net and need to find its dimensions (length, width, height). 2. **Identify the faces and their areas:** The net shows 6 rectangles with areas: 72 m² (2 faces), 36 m² (2 faces), and 18 m² (2 faces). 3. **Recall the surface area formula for a rectangular prism:** $$\text{Surface Area} = 2(lw + lh + wh)$$ where $l$, $w$, and $h$ are the length, width, and height. 4. **Assign variables to dimensions:** Let the dimensions be $l$, $w$, and $h$. 5. **Relate areas to dimensions:** Each face area corresponds to a product of two dimensions: - Two faces of area 72 m²: $lw = 72$ - Two faces of area 36 m²: $lh = 36$ - Two faces of area 18 m²: $wh = 18$ 6. **Use the equations to find dimensions:** From $lw = 72$ and $lh = 36$, divide the two: $$\frac{lw}{lh} = \frac{72}{36} = 2$$ $$\Rightarrow \frac{w}{h} = 2$$ 7. **Express $w$ in terms of $h$:** $$w = 2h$$ 8. **Use $wh = 18$ to find $h$:** $$w h = 18$$ Substitute $w = 2h$: $$2h \times h = 18$$ $$2h^2 = 18$$ $$h^2 = 9$$ $$h = 3$$ (taking positive value since length is positive) 9. **Find $w$:** $$w = 2h = 2 \times 3 = 6$$ 10. **Find $l$ using $lw = 72$:** $$l \times 6 = 72$$ $$l = \frac{72}{6} = 12$$ 11. **Final dimensions:** $$l = 12, w = 6, h = 3$$ These dimensions satisfy all given face areas. **Answer:** The dimensions of the rectangular prism are 12 m, 6 m, and 3 m.