To calculate the perimeter of the rectangle, we need to identify the length and width based on the information given.
- Length of the rectangle: This is given as \(2x\).
- 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 = \(12x + 6\)
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