To solve this problem, let's follow a step-by-step approach to find the expression representing the perimeter of the second rectangle and then combine it with the perimeter of the first rectangle.
1. Given Expressions:
- First rectangle perimeter: \( 6x + 8 \)
- Second rectangle perimeter: Out of the options provided, we need to select the correct one. The correct perimeter expression for the second rectangle is: \( 18x + 4y + 7 \)
2. Combine the two perimeters:
- First rectangle perimeter: \( 6x + 8 \)
- Second rectangle perimeter: \( 18x + 4y + 7 \)
To find the combined perimeter, we add the two expressions:
[tex]\[
(6x + 8) + (18x + 4y + 7)
\][/tex]
3. Perform the Addition:
- Combine like terms:
- \( 6x \) and \( 18x \) are like terms.
- \( 8 \) and \( 7 \) are constants.
- \( 4y \) remains as is since there is no corresponding \( y \) term in the first expression.
[tex]\[
6x + 18x + 4y + 8 + 7
\][/tex]
Simplify the expression:
[tex]\[
(6x + 18x) + 4y + (8 + 7) = 24x + 4y + 15
\][/tex]
Therefore, the combined perimeter of the two rectangles is:
[tex]\[
24x + 4y + 15
\][/tex]
