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:
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\( P = 2(5) + 2(9) \) 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)
-
\( P = 2(x + 3) \) 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)
-
\( P = 2(l + w) \) units:
- This is the perimeter formula stated directly. (Valid)
-
\( P = 4x \) 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)
-
\( P = 2l + 2w \) 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
2 answers