To find the perimeter of a rectangle, we use the formula:
\[ P = 2(\text{length} + \text{width}) \]
Given that the sides of the rectangle are represented by polynomials in terms of \(x\), let's assume:
- The length is \(l(x)\)
- The width is \(w(x)\)
The perimeter can be expressed as:
\[ P = 2(l(x) + w(x)) \]
However, the specific polynomial expressions for the length and width are not provided in your question. Assuming they are represented correctly in accordance with the answer choices you provided, we can analyze the potential combinations.
Let's consider two generic polynomials:
- Length \(l(x) = 9x + a\)
- Width \(w(x) = 9x + b\)
We combine the expressions:
\[ l(x) + w(x) = (9x + a) + (9x + b) = 18x + (a + b) \]
Then multiplying by 2 to find the perimeter:
\[ P = 2(18x + (a + b)) = 36x + 2(a + b) \]
Now, checking against the provided expressions:
- \(92x + 52\)
- \(9x + 5\)
- \(92x + 72\)
- \(9x + 7\)
The expressions to choose from do not directly resemble \(36x + k\) for any polynomial \(a\) and \(b\) resulting in the terms \(a + b\).
If we assume the perimeter sums match twice some polynomials:
Given none of the options are plausible unless we have exact polynomial formats as length and width, if they were meant to represent some known polynomials you need to key them in.
Conclusion
If you provide exact values for the rectangle's length and width in polynomial form, we can directly compute the perimeter. As it stands, we cannot choose among the options you provided without additional information about the specific expressions for length and width. Please clarify those for an accurate calculation.