To determine which expression represents the perimeter of the square, let's go through the steps required to find the perimeter given the side length.
1. Identify the side length of the square:
The expression given for the side length of the square is [tex]\( 4.8x + 2.4 \)[/tex].
2. Recall the formula for the perimeter of a square:
The perimeter [tex]\( P \)[/tex] of a square is given by [tex]\( P = 4 \times \text{side length} \)[/tex].
3. Substitute the given side length into the perimeter formula:
Given the side length [tex]\( 4.8x + 2.4 \)[/tex], the perimeter would be:
[tex]\[
P = 4 \times (4.8x + 2.4)
\][/tex]
4. Distribute the 4 to both terms inside the parentheses:
[tex]\[
P = 4 \times 4.8x + 4 \times 2.4
\][/tex]
5. Calculate the products:
[tex]\[
P = 19.2x + 9.6
\][/tex]
Thus, the expression that represents the perimeter of the square is [tex]\( 19.2x + 9.6 \)[/tex].
Now, look at the options provided:
A. [tex]\( 4.8x + 2.4 + 4 \)[/tex]
B. [tex]\( 19.2x + 2.4 \)[/tex]
C. [tex]\( 8(2.4x + 1.2) \)[/tex]
D. [tex]\( 4.8x + 9.6 \)[/tex]
The correct answer matches the expression we derived. Therefore, the correct answer is not directly listed in the options. But recognizing the structure and applying corrections:
The expression we derived is: [tex]\(19.2x + 9.6\)[/tex] closest match but precisely it reflects:
- But closest to [tex]\(19.2 \)[/tex]:
The correct answer applies the precise mathematical logic leading towards interpreation error but directly reflects:
Correct steps lead to :
[tex]\( 19.2x + 9.6 \)[/tex]
Thus the dimensions reflect into match close yet precise.
