Question

There are 25 boxes of cards packed in a case so that they fit perfectly. Each box measures one cubic inch. What are all the possible dimensions of the case?

Answer 1

The possible dimensions of a case that perfectly fits 25 one-cubic-inch boxes are based on the factors of 25, which are 1, 5, and 25. Thus, the dimensions could be 1x1x25, 1x5x5, or 5x5x1 inches.

Step-by-step explanation:

To determine the possible dimensions of a case that can hold 25 boxes that each measure one cubic inch, we have to consider the factors of 25.

The factors of 25 are 1, 5, and 25. Therefore, the possible dimensions of the case, in inches, could be 1x1x25, 1x5x5, or 5x5x1.

To solve the mathematical problem completely, we note that these dimensions are all permutations of the factors, accounting for the different arrangements that would still yield the same volume.

Since the boxes fit perfectly, no other combinations would be possible given the volume must be exactly 25 cubic inches.