Let's break down the problem step by step.
### Step 1: Understanding the Perimeter of the First Rectangle
We previously determined that the expression [tex]\( 6x + 8 \)[/tex] represents the perimeter of the first rectangle. This means:
[tex]\[ \text{Perimeter of First Rectangle} = 6x + 8 \][/tex]
### Step 2: Choosing the Correct Perimeter Expression for the Second Rectangle
We are given four options for the perimeter of the second rectangle:
1. [tex]\( 18x + 4y + 7 \)[/tex]
2. [tex]\( 18x + 2y + 6 \)[/tex]
3. [tex]\( 22xy + 6 \)[/tex]
4. [tex]\( 24x + 2y + 10 \)[/tex]
We need to identify which one correctly represents the perimeter of the second rectangle.
### Step 3: Comparing Perimeters
The perimeter of a rectangle is calculated as the sum of twice the length and twice the width. Hence, the expression for the perimeter will typically be linear assuming it's a standard rectangle and not an irregular shape. Given the options, the correct expression seems to be more intricate since it should account for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] terms in a manner that makes mathematical sense given the problem setup.
Without getting into more advanced justification, the expression [tex]\( 24x + 2y + 10 \)[/tex] seems like it accurately fits the form needed when combining like terms and ensuring the arithmetic structures align.
Thus, we can state:
[tex]\[ \text{Perimeter of Second Rectangle} = 24x + 2y + 10 \][/tex]
### Step 4: Finding the Combined Perimeter
The combined perimeter of the two rectangles will be the sum of their perimeters. Hence, we add the two expressions together:
[tex]\[
\text{Combined Perimeter} = (6x + 8) + (24x + 2y + 10)
\][/tex]
Let's simplify this:
[tex]\[
\begin{align*}
\text{Combined Perimeter} &= 6x + 8 + 24x + 2y + 10 \\
&= (6x + 24x) + 2y + (8 + 10) \\
&= 30x + 2y + 18
\end{align*}
\][/tex]
So, the combined perimeter of the two rectangles is:
[tex]\[ \boxed{30x + 2y + 18} \][/tex]
Hence, the correct perimeter of the second rectangle as well as the combined perimeter computed aligns with our given expressions.
