A rectangle has sides whose lengths in units are represented by polynomials as shown, where x is a positive integer.

Question

Which expression represents the perimeter of the rectangle in units?

(1 point)
Responses

92x+52
9 halves x plus 5 halves

9x+5
9 x plus 5

92x+72
9 halves x plus 7 halves

9x+7
9 x plus 7
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Answer 1

To find the perimeter of a rectangle, you can use the formula:

\[ \text{Perimeter} = 2(\text{Length} + \text{Width}) \]

Let's define the length and width of the rectangle using the polynomials given. However, since the specific polynomials for the sides are not provided in your question, I will provide a general method to find the perimeter based on any given polynomial expressions for the length and width.

1. Let the length of the rectangle be represented by \(L\).
2. Let the width of the rectangle be represented by \(W\).
3. Then, the perimeter \(P\) can be expressed as: \[ P = 2(L + W) \]

If we use specific polynomial expressions for \(L\) and \(W\):

• For example, if \(L = 9x + 5\) and \(W = 9x + 7\), then:

\[ P = 2((9x + 5) + (9x + 7)) \] \[ = 2(18x + 12) \] \[ = 36x + 24 \]

However, since we don't have specific definitions for \(L\) and \(W\), we cannot compute an exact numerical expression for the perimeter without additional information.

To select the correct option, you need to choose from:

• \(92x + 52\)
• \(9x + 5\)
• \(92x + 72\)
• \(9x + 7\)

Please provide the specific expressions for the length and width of the rectangle to determine the exact perimeter expression.