1. **Problem 1: Find the volume of the rectangular prism with dimensions 5 cm, 10 cm, and 2 cm.** The volume $V$ of a rectangular prism is given by the formula: $$V = \text{length} \times \text{width} \times \text{height}$$ 2. Substitute the given dimensions: $$V = 5 \times 10 \times 2$$ 3. Calculate the product: $$V = 100$$ 4. The volume is $100$ cubic centimeters, so the correct answer is **D 100 cm^3**. 5. **Problem 2: Determine which triangle is similar to the given triangle with sides 8, 6, and 12.** Two triangles are similar if their corresponding sides are in proportion. 6. Calculate the ratios of the given triangle's sides: $$\frac{8}{6} = 1.333, \quad \frac{12}{6} = 2$$ 7. Check each option for proportional sides: - Option A sides: 10, 16, 20 - Ratios to 6: $\frac{10}{6} = 1.666$, $\frac{16}{6} = 2.666$, $\frac{20}{6} = 3.333$ (not matching 1.333 and 2) - Option B sides: 10, 7, 6 - Ratios to 6: $\frac{10}{6} = 1.666$, $\frac{7}{6} = 1.166$, $\frac{6}{6} = 1$ (not matching) - Option C sides: 8, 4, 6 - Ratios to 6: $\frac{8}{6} = 1.333$, $\frac{4}{6} = 0.666$, $\frac{6}{6} = 1$ (not matching all ratios) - Option D sides: 14, 22, 20 - Ratios to 6: $\frac{14}{6} = 2.333$, $\frac{22}{6} = 3.666$, $\frac{20}{6} = 3.333$ (not matching) 8. None of the options have all side ratios equal to the given triangle's side ratios, so no triangle is similar based on side lengths alone. However, Option A has a side 20 which is close to the largest side 12 scaled by a factor of about 1.666, but the other sides do not match proportionally. **Final answers:** - Volume of rectangular prism: $100$ cm$^3$ (Option D) - No triangle option is similar based on side length ratios.