1. **State the problem:** We have a rectangle with an original length of 8 cm and an area of 20 cm². We want to find the original width, then analyze what happens when the length is increased by 2 cm and the area increases by 4 cm². Finally, we check if the width decreases by less than 5% as Noah claims. 2. **Find the original width:** The area of a rectangle is given by $$\text{Area} = \text{Length} \times \text{Width}$$ Given the original area is 20 cm² and length is 8 cm, we solve for width: $$\text{Width} = \frac{\text{Area}}{\text{Length}} = \frac{20}{8} = 2.5 \text{ cm}$$ 3. **Find the new length and new area:** The length is increased by 2 cm: $$\text{New Length} = 8 + 2 = 10 \text{ cm}$$ The area is increased by 4 cm²: $$\text{New Area} = 20 + 4 = 24 \text{ cm}^2$$ 4. **Find the new width:** Using the new area and new length: $$\text{New Width} = \frac{\text{New Area}}{\text{New Length}} = \frac{24}{10} = 2.4 \text{ cm}$$ 5. **Calculate the percentage decrease in width:** The width decreased from 2.5 cm to 2.4 cm, so the decrease is: $$\text{Decrease} = 2.5 - 2.4 = 0.1 \text{ cm}$$ Percentage decrease is: $$\frac{0.1}{2.5} \times 100 = 4\%$$ 6. **Conclusion:** Since the width decreases by 4%, which is less than 5%, Noah is correct. **Final answer:** Noah's statement that the width decreases by less than 5% is correct.