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

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