Answered

The width of a rectangle measures [tex]\((k+3)\)[/tex] centimeters, and its length measures [tex]\((k-9)\)[/tex] centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

A. [tex]\(-8 + 4k\)[/tex]
B. [tex]\(8k - 16\)[/tex]
C. [tex]\(2k - 6\)[/tex]
D. [tex]\(-12 + 4k\)[/tex]



Answer :

GinnyAnswer
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.

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