A rectangle is decomposed into nine squares whose bases measure 1, 4, 7, 8, 9, 10, 14, 15, and 18 units respectively. What are the dimensions of the rectangle?

The total area is:

18^{2} + 15^{2} + 14^{2} + 10^{2} + 9^{2} + 8^{2} + 7^{2} + 4^{2} + 1^{2} = 1056.

This can be factored into 33 x 32, and the squares fit as shown.