To determine the perimeter of a rectangle, we'll use the formula for the perimeter of a rectangle, which is:
[tex]\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \][/tex]
Given:
- The width of the rectangle is [tex]\((9s + 6)\)[/tex] centimeters.
- The length of the rectangle is [tex]\((s + 1)\)[/tex] centimeters.
Let's apply these values to the perimeter formula step-by-step:
1. Substitute the given expressions into the perimeter formula:
[tex]\[
\text{Perimeter} = 2 \times \left((s + 1) + (9s + 6)\right)
\][/tex]
2. Combine the expressions inside the parentheses:
[tex]\[
(s + 1) + (9s + 6) = s + 1 + 9s + 6
\][/tex]
3. Simplify the combined expression:
[tex]\[
s + 9s + 1 + 6 = 10s + 7
\][/tex]
4. Multiply the simplified expression by 2:
[tex]\[
2 \times (10s + 7) = 2 \times 10s + 2 \times 7 = 20s + 14
\][/tex]
Therefore, the expression that represents the perimeter, in centimeters, of the rectangle is:
[tex]\[\boxed{20s + 14}\][/tex]
This matches the given multiple-choice answer:
[tex]\[ \boxed{14 + 20s} \][/tex]
