1. **State the problem:** We have a rectangle with length $127.3$ cm and width $86.5$ cm, both measured to 1 decimal place. We need to find the upper and lower bounds for the perimeter. 2. **Recall the formula for perimeter of a rectangle:** $$P = 2(\text{length} + \text{width})$$ 3. **Understand bounds for measurements:** - Since length and width are correct to 1 decimal place, the possible error is $\pm 0.05$ cm. - Therefore, the lower bound for length is $127.3 - 0.05 = 127.25$ cm. - The upper bound for length is $127.3 + 0.05 = 127.35$ cm. - Similarly, the lower bound for width is $86.5 - 0.05 = 86.45$ cm. - The upper bound for width is $86.5 + 0.05 = 86.55$ cm. 4. **Calculate the lower bound for perimeter:** $$P_{lower} = 2(127.25 + 86.45) = 2(213.7) = 427.4 \text{ cm}$$ 5. **Calculate the upper bound for perimeter:** $$P_{upper} = 2(127.35 + 86.55) = 2(213.9) = 427.8 \text{ cm}$$ 6. **Final answer:** - Lower bound for perimeter: $427.4$ cm - Upper bound for perimeter: $427.8$ cm This means the true perimeter lies between $427.4$ cm and $427.8$ cm.