Question

Consider the rectangle below.

2x

4x+3

(3 points)


Length of the rectangle =

Width of rectangle =

The perimeter of the rectangle is
. Remember to simplify the expression.

Answer 1

To calculate the perimeter of the rectangle, we need to identify the length and width based on the information given.

1. **Length of the rectangle**: This is given as \(2x\).
2. **Width of the rectangle**: This is given as \(4x + 3\).

The formula for the perimeter \(P\) of a rectangle is given by:

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

Now, substituting the values for length and width:

\[
P = 2 \times (2x + (4x + 3))
\]

Simplifying the expression inside the parentheses:

\[
P = 2 \times (2x + 4x + 3) = 2 \times (6x + 3)
\]

Now, distribute the 2:

\[
P = 12x + 6
\]

Thus, the perimeter of the rectangle, simplified, is:

\[
\text{The perimeter of the rectangle is } 12x + 6.
\]

In summary:
- **Length of the rectangle** = \(2x\)
- **Width of the rectangle** = \(4x + 3\)
- **The perimeter of the rectangle is** = \(12x + 6\)