Answer:

The largest integer that could be the length of an edge of the box is 6.

Step-by-step explanation:

The volume of the rectangular box is 48.

The sum of the length of the twelve edges of the box is 48.

Divide both sides by 4.

The factors of 48 are 1,2,3,4,6,8,12,16,24,48. Since the sum of side lengths are 12, therefore the possible integers for the side length are 1,2,3,4,6,8.

Since

and

Therefore the side lengths are 2,4,6 and the largest integer that could be the length of an edge of the box is 6.