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?

Question

anonymous · Answer

Lets draw a picture:
|dw:1372627793144:dw|
Since the larger one has 8 moer square feet than the smaller, we know that the area of the smaller plus 8 equals the area of the larger one. So:
$$2w+w^2 +8=4w+w^2$$ Doing a little algebra we find:
$$8=2w$$
Or, the width is 4 feet.