4 The length of a rectangular rug is 4 less than twice its width. The perimeter of the rug is 40 feet. Part A Write a system of equations that can be used to find the length, I, and width w,of the rug, in feet. Answer: Part B What is the area of the rug? Show your work. Answer: - square feet

## Step 1
The problem provides two pieces of information: the relationship between the length and the width of the rectangular rug, and the perimeter of the rug. We can translate this information into a system of equations.

## Step 2
The first equation comes from the relationship between the length and the width of the rectangular rug. The problem states that the length is 4 less than twice the width. This can be written as:
### $l = 2w - 4$

## Step 3
The second equation comes from the definition of the perimeter of a rectangle. The perimeter is the sum of all the sides of the rectangle. Since a rectangle has two pairs of equal sides, the perimeter is twice the sum of the length and the width. The problem states that the perimeter is 40 feet, so we can write this as:
### $2l + 2w = 40$

## Step 4
For part B, we need to find the area of the rectangular rug. The area of a rectangle is given by the product of its length and width. We can substitute the expression for $l$ from the first equation into the area formula to get:
### $A = w(2w - 4)$

## Step 5
We can then solve this equation for $w$ by setting it equal to the given perimeter and solving for $w$. Once we have the value of $w$, we can substitute it back into the equation for $A$ to find the area.