1. **State the problem:** We have a triangle with sides 5.2 cm, 6.3 cm, and 9.4 cm, each measured to the nearest millimeter (0.1 cm). We need to find the lower bound of the perimeter. 2. **Understanding bounds:** When a measurement is given to the nearest 0.1 cm, the actual length can be as low as $\text{measurement} - 0.05$ cm and as high as $\text{measurement} + 0.05$ cm. 3. **Calculate the lower bound of each side:** - Side 1: $5.2 - 0.05 = 5.15$ cm - Side 2: $6.3 - 0.05 = 6.25$ cm - Side 3: $9.4 - 0.05 = 9.35$ cm 4. **Calculate the lower bound of the perimeter:** $$\text{Lower bound perimeter} = 5.15 + 6.25 + 9.35 = 20.75 \text{ cm}$$ 5. **Conclusion:** The lower bound of the perimeter of the triangle is **20.75 cm**.