To find the dimensions of the largest acceptable box with square ends, we need to consider the given condition that the sum of the length and girth should be at most 108 inches.
Let's assume that the length of the box is x inches.
Since the box has square ends, the width and height will also be x inches.
The girth of the box is the distance around it, which can be calculated by adding the sum of the two equal sides of the box twice.
So, the girth can be calculated as: 2 * (width + height)
Since the width and height are both x inches, the girth is: 2 * (x + x) = 4x
Now, according to the given condition, the sum of the length and girth should be at most 108 inches:
x + 4x ≤ 108
Simplifying the equation:
5x ≤ 108
Dividing both sides of the equation by 5:
x ≤ 21.6
Since the dimensions of a box cannot be a fraction, we need to round down the value of x to the nearest whole number.
Therefore, the maximum value for x is 21.
So, the dimensions of the largest acceptable box with square ends are 21 inches in length, 21 inches in width, and 21 inches in height.