1. **Problem statement:** We have two rectangular prisms (storage containers) with given dimensions and need to find missing measurements. 2. **Formula for volume of a rectangular prism:** $$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ 3. **Part (a):** Given volume = 69 ft³, width = 3 ft, height = 4 ft, find length. 4. Substitute known values into the volume formula: $$69 = \text{length} \times 3 \times 4$$ 5. Simplify the multiplication: $$69 = \text{length} \times 12$$ 6. To isolate length, divide both sides by 12: $$\text{length} = \frac{69}{12}$$ 7. Show cancellation: $$\text{length} = \frac{\cancel{69}}{\cancel{12}} = \frac{69}{12}$$ (Note: 69 and 12 share a common factor 3, so simplify further) 8. Simplify fraction: $$\text{length} = \frac{69 \div 3}{12 \div 3} = \frac{23}{4} = 5.75$$ 9. **Answer for (a):** Length = 5.75 ft 10. **Part (b):** Given base area = 15 ft², height = 1/4 ft, find volume. 11. Volume formula using base area: $$\text{Volume} = \text{Base Area} \times \text{height}$$ 12. Substitute known values: $$\text{Volume} = 15 \times \frac{1}{4}$$ 13. Multiply: $$\text{Volume} = \frac{15}{4} = 3.75$$ 14. **Answer for (b):** Volume = 3.75 ft³