Final answer:
The maximum possible width of the banner is 6 feet, assuming a length of 18 feet and a maximum of 48 feet of trim available for the border. The width can be any value less than or equal to 6 feet.
Step-by-step explanation:
The student is dealing with a perimeter problem in geometry. To find the possible widths of a rectangular banner that is 18 feet long with a total of no more than 48 feet of trim for the entire border, we must first understand that the perimeter of the rectangle is the sum of all its sides.
Since the length (L) is given as 18 feet, and there are two lengths and two widths (W) in the perimeter (P), we can express this as the equation P = 2L + 2W. Substituting the known values, we get 48 = 2(18) + 2W, which simplifies to 48 = 36 + 2W. Then, to solve for W, we subtract 36 from both sides to get 12 = 2W, and finally divide by 2 to find W = 6.
Therefore, the maximum width is 6 feet, keeping in mind that the width could be any measurement smaller than this, as it would still be covered by the 48 feet of trim available. Selecting the appropriate unit of measurement, which in this case is feet for such large dimensions, is crucial for accurate results.