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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 determine the expression that represents the perimeter of the given rectangle, let's follow these steps:

1. Identify the expressions given for the width and length of the rectangle:
- Width: [tex]\(k + 3\)[/tex] cm
- Length: [tex]\(k - 9\)[/tex] cm

2. Recall the formula for the perimeter of a rectangle:
[tex]\[ P = 2(\text{width} + \text{length}) \][/tex]

3. Substitute the given expressions for width and length into the perimeter formula:
[tex]\[ P = 2((k + 3) + (k - 9)) \][/tex]

4. Simplify the expression inside the parentheses:
[tex]\[ (k + 3) + (k - 9) = k + k + 3 - 9 = 2k - 6 \][/tex]

5. Multiply the simplified expression by 2:
[tex]\[ P = 2 \times (2k - 6) = 4k - 12 \][/tex]

6. Match the simplified perimeter expression with the provided choices:
- [tex]\( -8 + 4k \)[/tex]
- [tex]\( 8k - 16 \)[/tex]
- [tex]\( 2k - 6 \)[/tex]
- [tex]\( -12 + 4k \)[/tex]

The expression [tex]\(4k - 12\)[/tex] matches the form of the last choice, [tex]\(-12 + 4k\)[/tex].

So, the correct answer is:
[tex]\[ \boxed{-12 + 4k} \][/tex]

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