24888

32X33
First I found the area of the big rectangle by adding together the area of all the squares (1056). I then found the prime factor of 1056, 11X3X2X2X2X2X2. I then found all the different ways you can split these up eg. 11X3 and 2X2X2X2X2. These are all the possible sides. Because the 18 by 18 square will take up 18cm each side the rectangle needs to be at least 18 cm each side. This left me with 3 different possibilities: 33x32 22x48 44x24
I then made a paper copy of the puzzle and tried each of the different dimensions until I got an answer.