If a rectangle has a length that is twice its width, what is the relationship between its perimeter and area?

If a rectangle has a length that is twice its width, what is the relationship between its perimeter and area?

• A. Perimeter is greater than area.
• B. Perimeter equals area.
• C. Area is greater than perimeter.
• D. Cannot be determined.

Answer: (A)

To determine the relationship between the perimeter and area of a rectangle in which the length is twice its width, let's define the width as \( w \). Consequently, the length would be \( 2w \). The perimeter \( P \) of a rectangle is calculated using the formula: \[ P = 2(\text{length} + \text{width}) \] Substituting in our variables: \[ P = 2(2w + w) = 2(3w) = 6w \] Next, the area \( A \) of the rectangle is calculated using the formula: \[ A = \text{length} \times \text{width} \] Substituting again: \[ A = 2w \times w = 2w^2 \] Now, to compare the perimeter with the area, we need to express both in terms of \( w \). We see that: - The perimeter \( P \) is \( 6w \), - The area \( A \) is \( 2w^2 \). To find the relationship between perimeter and area, we can compare \( P \) and \( A \): 1. Consider \( 6w \) and

To determine the relationship between the perimeter and area of a rectangle in which the length is twice its width, let's define the width as ( w ). Consequently, the length would be ( 2w ).

The perimeter ( P ) of a rectangle is calculated using the formula:

[ P = 2(\text{length} + \text{width}) ]

Substituting in our variables:

[ P = 2(2w + w) = 2(3w) = 6w ]

Next, the area ( A ) of the rectangle is calculated using the formula:

[ A = \text{length} \times \text{width} ]

Substituting again:

[ A = 2w \times w = 2w^2 ]

Now, to compare the perimeter with the area, we need to express both in terms of ( w ).

We see that:

• The perimeter ( P ) is ( 6w ),

• The area ( A ) is ( 2w^2 ).

To find the relationship between perimeter and area, we can compare ( P ) and ( A ):

1. Consider ( 6w ) and