Two rectangles have the same width. The length of one is 2 feet longer than the width. The length of the other is 4 feet longer than the width. The larger rectangle has 8 more square feet than the smaller. What is the width of the rectangles?

w(w+2)+8 = w(w+4)

w^2+2w+8 = w^2+4w
2w = 8
w = 4

The rectangles are
4x6 and 4x8
The areas are 24 and 32, which differ by 8.

Let's break down the given information step by step to find the width of the rectangles.

1. Let's assume the width of both rectangles is 'w'.

2. The length of the first rectangle is 2 feet longer than the width, so its length would be 'w + 2'.

3. The length of the second rectangle is 4 feet longer than the width, so its length would be 'w + 4'.

4. The larger rectangle has 8 more square feet than the smaller rectangle. To find the area of a rectangle, we multiply its length by its width. So, the equation for the larger rectangle's area would be:

(w + 4) * w = smaller rectangle's area + 8

Now, let's solve the equation to find the value of 'w', which represents the width of the rectangles.

(w + 4) * w = w * (w + 2) + 8

w^2 + 4w = w^2 + 2w + 8

Subtracting w^2 from both sides, we get:

4w = 2w + 8

Subtracting 2w from both sides, we get:

2w = 8

Dividing both sides by 2, we find:

w = 4

Therefore, the width of the rectangles is 4 feet.