To find the expression that represents the perimeter of a rectangle, we need to follow these steps:
1. Understand the Definitions:
- The width of the rectangle is given as [tex]\( k + 3 \)[/tex] centimeters.
- The length of the rectangle is given as [tex]\( k - 9 \)[/tex] centimeters.
2. Formula for Perimeter:
- The perimeter [tex]\( P \)[/tex] of a rectangle is given by the formula:
[tex]\[
P = 2(\text{length} + \text{width})
\][/tex]
3. Substitute the Given Expressions into the Formula:
- Substitute the width [tex]\( k + 3 \)[/tex] and the length [tex]\( k - 9 \)[/tex] into the perimeter formula:
[tex]\[
P = 2((k - 9) + (k + 3))
\][/tex]
4. Simplify Inside the Parentheses:
- Combine like terms inside the parentheses:
[tex]\[
(k - 9) + (k + 3) = k + k - 9 + 3 = 2k - 6
\][/tex]
5. Multiply by 2:
- Now multiply the simplified expression by 2 to find the perimeter:
[tex]\[
P = 2(2k - 6) = 4k - 12
\][/tex]
Therefore, the expression that represents the perimeter of the rectangle is:
[tex]\[
\boxed{-12 + 4k}
\][/tex]
This matches one of the provided answer choices exactly.
