To find the length of ribbon needed to go all the way around the edge of the rectangular top of the box, we need to calculate the perimeter of the rectangle.
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (length + width) \]
In this case, the dimensions of the top of the box are 140 mm and 230 mm.
- Calculate the perimeter in mm:
\[ P = 2 \times (140 \text{ mm} + 230 \text{ mm}) \] \[ P = 2 \times 370 \text{ mm} \] \[ P = 740 \text{ mm} \]
- Convert the perimeter from millimeters to centimeters:
Since \( 1 , \text{cm} = 10 , \text{mm} \), we divide the perimeter in mm by 10 to convert to cm:
\[ P = \frac{740 \text{ mm}}{10} = 74 \text{ cm} \]
Thus, the length of ribbon needed to go all the way around the edge of the top of the box is 74 cm.
Therefore, the correct answer is: 74 cm.