1. **State the problem:** We have a cuboid with length $L$ cm, width $W$ cm, and height $H$ cm. The net of the cuboid shows dimensions: total horizontal length $37.8$ cm and vertical height $20.1$ cm. The ratio of width to length is given as $W : L = 1 : 2$. We need to find $L$, $W$, and $H$. 2. **Understand the net:** The net consists of rectangles arranged linearly. The total horizontal length of the net is $37.8$ cm, which is the sum of the lengths of three rectangles: $L + L + W = 2L + W$. The total vertical height is $20.1$ cm, which corresponds to $H + W$. 3. **Use the ratio:** Given $W : L = 1 : 2$, we can write $W = \frac{1}{2}L$. 4. **Set up equations:** From horizontal length: $$2L + W = 37.8$$ Substitute $W = \frac{1}{2}L$: $$2L + \frac{1}{2}L = 37.8$$ 5. **Simplify and solve for $L$:** $$2L + \frac{1}{2}L = \frac{4}{2}L + \frac{1}{2}L = \frac{5}{2}L = 37.8$$ Multiply both sides by $\frac{2}{5}$: $$L = 37.8 \times \frac{2}{5}$$ $$L = \cancel{37.8} \times \frac{2}{\cancel{5}} = 15.12$$ 6. **Find $W$ using the ratio:** $$W = \frac{1}{2}L = \frac{1}{2} \times 15.12 = 7.56$$ 7. **Find $H$ using vertical height:** $$H + W = 20.1$$ Substitute $W = 7.56$: $$H + 7.56 = 20.1$$ $$H = 20.1 - 7.56 = 12.54$$ **Final answers:** $$L = 15.12 \text{ cm}$$ $$W = 7.56 \text{ cm}$$ $$H = 12.54 \text{ cm}$$