1. **Stating the problem:** We have two rectangular prisms side by side with given surface areas and volumes, and we need to find the unknown lengths. 2. **Given data:** - Left prism: Area $A_1 = 35$ cm², Volume $V_1 = 385$ cm³ - Right prism: Area $A_2 = 48$ cm², Volume $V_2 = 720$ cm³ 3. **Formula for rectangular prism:** - Surface area $A = 2(lw + lh + wh)$ - Volume $V = lwh$ 4. **Step 1: Find dimensions for each prism.** Since the problem shows question marks for unknown lengths, assume the base dimensions are known or can be derived from the cubes' areas. 5. **Analyzing the cubes:** - Cube areas: 81, 16, 64, 100 cm² - Side lengths of cubes are $ \sqrt{81} = 9$, $ \sqrt{16} = 4$, $ \sqrt{64} = 8$, $ \sqrt{100} = 10$ 6. **Using the numbers 5 and 6 near cubes:** These likely represent heights or lengths related to the prisms. 7. **Calculate unknown length for left prism:** Given $V_1 = 385$ cm³ and $A_1 = 35$ cm². Assuming the base area $B_1$ and height $h_1$ satisfy: $$V_1 = B_1 \times h_1$$ $$A_1 = 2(B_1 + P_1 h_1)$$ where $P_1$ is the perimeter of the base. Since exact base dimensions are not given, use volume and area to find $h_1$: Try $h_1 = \frac{V_1}{B_1}$. 8. **Similarly for right prism:** $$h_2 = \frac{V_2}{B_2}$$ 9. **Final answer:** Without explicit base dimensions, the unknown lengths (heights) are: $$h_1 = \frac{385}{B_1}$$ $$h_2 = \frac{720}{B_2}$$ If base areas $B_1$ and $B_2$ correspond to the cube areas (e.g., 7x5=35 for left prism base), then: - Left prism length $l_1 = \frac{385}{35} = 11$ cm - Right prism length $l_2 = \frac{720}{48} = 15$ cm **Therefore, the unknown lengths are 11 cm for the left prism and 15 cm for the right prism.**