Question

Consider the rectangle below.
One says 4x+3
The other says 2x


(3 points)
7th Grade Math Formula Sheet

Length of the rectangle =

Width of rectangle =

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

Answer 1

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)