To find the dimensions of the rectangle and its perimeter based on the given information, we have:
- Length = \( 4x + 3 \)
- Width = \( 2x \)
Perimeter of a Rectangle
The formula for the perimeter \( P \) of a rectangle is: \[ P = 2 \times (\text{Length} + \text{Width}) \]
Substitute the Values
Substituting in our length and width: \[ P = 2 \times ((4x + 3) + (2x)) \]
Combine Like Terms
First, we combine the terms inside the parentheses: \[ 4x + 3 + 2x = 6x + 3 \]
Substitute Back into the Perimeter Formula
Now we substitute this back into the perimeter formula: \[ P = 2 \times (6x + 3) \]
Distribute the 2
Now, distribute the 2: \[ P = 2 \times 6x + 2 \times 3 = 12x + 6 \]
Final Answer
Thus, the perimeter of the rectangle is: \[ P = 12x + 6 \]
Summary
- Length of the rectangle = \( 4x + 3 \)
- Width of the rectangle = \( 2x \)
- The perimeter of the rectangle = \( 12x + 6 \) (simplified expression)