What is the expression for the perimeter P of a rectangle in terms of length l and width w?

What is the expression for the perimeter P of a rectangle in terms of length l and width w?

• A. P = l + w
• B. P = 2l + w
• C. P = 2l + 2w
• D. P = 2(l + w)

Answer: (C)

The perimeter \( P \) of a rectangle is calculated by adding together the lengths of all four sides. A rectangle has two lengths and two widths. Therefore, the perimeter can be expressed mathematically as: \[ P = l + l + w + w \] This simplifies to: \[ P = 2l + 2w \] This formulation clearly shows that you take the length \( l \) and multiply it by 2 since there are two equal sides of length \( l \). Similarly, you take the width \( w \) and also multiply it by 2 because there are two equal sides of width \( w \). Hence, the expression \( P = 2l + 2w \) captures the total length of all sides of the rectangle. Furthermore, it's worth noting that the expression can also be factored into a single expression, which is \( P = 2(l + w) \). Both \( 2l + 2w \) and \( 2(l + w) \) convey the same perimeter concept, but the former is a more direct computation showing the contributions of lengths and widths separately. So, the correct choice reflects the accurate computation of a rectangle's perimeter.

The perimeter ( P ) of a rectangle is calculated by adding together the lengths of all four sides. A rectangle has two lengths and two widths. Therefore, the perimeter can be expressed mathematically as:

[

P = l + l + w + w

]

This simplifies to:

[

P = 2l + 2w

]

This formulation clearly shows that you take the length ( l ) and multiply it by 2 since there are two equal sides of length ( l ). Similarly, you take the width ( w ) and also multiply it by 2 because there are two equal sides of width ( w ). Hence, the expression ( P = 2l + 2w ) captures the total length of all sides of the rectangle.

Furthermore, it's worth noting that the expression can also be factored into a single expression, which is ( P = 2(l + w) ). Both ( 2l + 2w ) and ( 2(l + w) ) convey the same perimeter concept, but the former is a more direct computation showing the contributions of lengths and widths separately. So, the correct choice reflects the accurate computation of a rectangle's perimeter.