Final answer:
To find the possible range of values for the width of the banquet hall, we need to consider the total area of the four walls and the ceiling. By setting up an inequality and solving for the width, we find that the possible range of values for the width is 0 m ≤ w ≤ 8.125 m.
Step-by-step explanation:
To find the possible range of values for the width of the banquet hall, we need to consider the total area of the four walls and the ceiling. The formula for the total surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
Given that the height is 7m and the length is 21m, we can substitute these values into the formula:
Surface Area = 2(21)(7) + 2(21)(w) + 2(w)(7)
Simplifying this equation gives us:
Surface Area = 294 + 42w + 14w
Since the total area is not greater than 749m², we can set up the inequality:
294 + 42w + 14w ≤ 749
Combining like terms and solving for w, we get:
56w ≤ 455
w ≤ 8.125
Therefore, the possible range of values for the width is 0 cm ≤ w ≤ 8.125 cm. Since the options provided are in meters, we can convert this range to meters, which gives us 0 m ≤ w ≤ 8.125 m.