To determine the upper bound for the perimeter of a rectangle, we must first establish the maximum possible measurements of its length and width, and then use these dimensions to compute the perimeter.
### Step 1: Determine the Upper Bound for the Length
The length is given as 24 cm, with a precision to the nearest centimeter. This suggests the length could be anywhere between 23.5 cm and 24.5 cm. To find the upper bound, we take the higher end of this range:
[tex]\[ \text{Maximum length} = 24.5 \text{ cm} \][/tex]
### Step 2: Determine the Upper Bound for the Width
The width is specified as 6.4 cm, accurate to the nearest millimeter. This places the range of the width from 6.35 cm to 6.45 cm. Hence, the upper bound will be the higher limit:
[tex]\[ \text{Maximum width} = 6.45 \text{ cm} \][/tex]
### Step 3: Compute the Upper Bound for the Perimeter
The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[ P = 2(\text{length} + \text{width}) \][/tex]
Substituting the maximum length and width into the formula:
[tex]\[ P = 2(24.5 \text{ cm} + 6.45 \text{ cm}) \][/tex]
Adding the dimensions inside the parentheses first:
[tex]\[ 24.5 \text{ cm} + 6.45 \text{ cm} = 30.95 \text{ cm} \][/tex]
Then, multiplying by 2 to account for both pairs of sides:
[tex]\[ P = 2 \times 30.95 \text{ cm} \][/tex]
[tex]\[ P = 61.9 \text{ cm} \][/tex]
Therefore, the upper bound for the perimeter of the rectangle is:
[tex]\[ \boxed{61.9 \text{ cm}} \][/tex]
