Final answer:
Possible dimensions for the rectangular area given by the equation 27x - 9 are found in Option D, a width of 9 and a length of 3x - 1, and Option E, a width of 3x - 1 and a length of 9. These combinations, when multiplied, equal the area equation given.
Step-by-step explanation:
Given the rectangular area equation Area = 27x - 9, we need to find possible dimensions. The area of a rectangle is found by multiplying its length and width. Therefore, if we have two factors that multiply to give 27x - 9, those can represent the possible dimensions of the rectangle.
Option A: A width of 27 and a length of x - 9 would multiply to 27(x - 9), which does not simplify to 27x - 9.
Option B: A width of x - 9 and a length of 27 would multiply to (x - 9)(27), which does not simplify to 27x - 9.
Option C: A width of 9 and a length of 27x - 1 would multiply to 9(27x - 1), which does not simplify to 27x - 9.
Option D: A width of 9 and a length of 3x - 1 would multiply to 9(3x - 1) = 27x - 9, which is the given area, so this is a correct dimension.
Option E: A width of 3x - 1 and a length of 9 would multiply to (3x - 1)(9) = 27x - 9, which is also the given area, so this is another correct dimension.
Option F: A width of 27x - 1 and a length of 9 would multiply to (27x - 1)(9), which does not simplify to 27x - 9.
Therefore, the correct dimensions that satisfy the area equation are found in Options D and E.