Question

The perimeter, P, of a rectangle is the sum of twice the length and twice the width.

P = 2(5)+2(9) units
P = 2(x+3) units
P = 2(l+w) units
P = 4 x units
P = 2l+ 2w units
choose all that apply

Answer 1

To identify which statements correctly represent the formula for the perimeter of a rectangle, we check each expression against the standard formula, which is:

\[ P = 2l + 2w \]

where \( l \) is the length and \( w \) is the width of the rectangle.

Here’s an analysis of each statement you provided:

1. **\( P = 2(5) + 2(9) \) units**:
- This calculates the perimeter for a rectangle with length 5 and width 9, specifically \( P = 10 + 18 = 28 \) units, which is correctly using the perimeter formula. **(Valid)**

2. **\( P = 2(x + 3) \) units**:
- This is in the form of the perimeter formula, assuming \( x + 3 \) is representing the sum of length and width (\( l + w \)). While it's not in the standard form, it's still a valid representation if \( x + 3 \) equates to \( l + w \). **(Valid)**

3. **\( P = 2(l + w) \) units**:
- This is the perimeter formula stated directly. **(Valid)**

4. **\( P = 4x \) units**:
- This implies that both the length and width are equal and equal to \( 2x \). This would not represent a general rectangle unless specified as a square. It is not a correct general representation of the perimeter formula. **(Not Valid)**

5. **\( P = 2l + 2w \) units**:
- This is the standard perimeter formula for a rectangle. **(Valid)**

In summary, the valid statements are:
- **\( P = 2(5) + 2(9) \) units**
- **\( P = 2(x + 3) \) units**
- **\( P = 2(l + w) \) units**
- **\( P = 2l + 2w \) units**