Final answer:
To find the length of one edge of the square base of the box (x), the total length of all 12 edges (144 inches) is divided by 12, resulting in x being 12 inches.
Step-by-step explanation:
The student is asked to determine the value of x, which represents the length of one edge of a square base of a cardboard box. The total length of all edges of the cardboard box, which has 12 edges, is given as 144 inches.
To solve for x, we must remember that a box has 4 edges on the base, 4 edges at the top (which are equal in length to the base edges since the box has a square base), and 4 vertical edges connecting the top and bottom (which have the same length). Since we know the total length of all edges combined is 144 inches, we can write the equation:
4x + 4x + 4x = 144
Combining like terms, we get:
12x = 144
Dividing both sides by 12 to isolate x:
x = 144 / 12
x = 12 inches
Therefore, the length of each edge of the square base of the box is 12 inches.