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?

Answer 1

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.