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Consider these rectangles:

Previously, we found that the expression \(6x + 8\) represents the perimeter of the first rectangle.

Now, find the expression that represents the perimeter of the second rectangle. Then use the two expressions to find the combined perimeter of the rectangles.

A. \(18x + 4y + 7\)

B. \(18z + 2y + 6\)

C. \(22xy + 6\)

D. [tex]\(24 \div 2y + 10\)[/tex]



Answer :

GinnyAnswer
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]

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