Question

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



Which expression represents the perimeter of the rectangle in units?


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, we use the formula:

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

If the lengths of the sides are represented by polynomials, let’s denote the length as \( L \) and the width as \( W \). The perimeter can be calculated as follows:

\[
\text{Perimeter} = 2 \times (L + W).
\]

In the options provided (which seem to have been cut off), we’re missing the specific polynomials for length and width. However, assuming the length \( L \) is represented by an expression like \( 9x + 5 \) and the width \( W \) by an expression like \( 9x + 7 \), then:

First, we calculate the sum of the length and width:

\[
L + W = (9x + 5) + (9x + 7) = 18x + 12.
\]

Next, we compute the perimeter:

\[
\text{Perimeter} = 2 \times (L + W) = 2 \times (18x + 12) = 36x + 24.
\]

However, since the specific expressions you referred to (for length and width) are not provided directly, if you provide those, I can directly compute the perimeter for those specific polynomials and find the corresponding answer from your response options.

If the polynomials were indeed \( 9x + 5 \) and \( 9x + 7 \), the perimeter is \( 36x + 24 \). Please clarify or provide the exact expressions for length and width if they differ from these assumed ones.