Our group of five girls split into two groups. One girl worked on Chandra's idea and worked out that if the total area of the rectangle was 1056 cm^2 then there were several possible shapes, but the largest square had a side length of 18 so obviously 2 by 528 is too narrow. Then she tried all the different possibilities and found that 33cm times 32cm was the only possible shape of the rectangle.
The other group were impressed with Brendan's idea and decided to try that. They put the 18 square in one corner and the 15 square next to it. Then they put the 14 square above the 18. Then working from the biggest squares down to the smallest and with a bit of trial and error they were able to fit them all in.
18 + 15 = 33 wide
18 + 14 = 32 long so the two solutions agreed with each other.