Squared rectangle

by David Radcliffe

The picture shows a rectangle that has been subdivided into nine squares. The area of the smallest square is 1. Can you find the areas of the other squares?

Squared RectangleAddendum: Anna Blinstein informs me that she has used this problem with great success as an end-of-year project for Algebra 1. Squared rectangles also make an appearance in the Exeter math problem sets.