Problem E

Three Squares

The three squares \(ABCD\), \(AEFG\), and \(AHJK\) overlap as shown in the diagram.

The side length of each square, in centimetres, is a positive integer. The area of square \(AEFG\) that is not covered by square \(ABCD\) is \(33\text{ cm}^2\). That is, the area of the shaded region \(BEFGDC\) is \(33\text{ cm}^2\). If \(DG = GK\), determine all possible side lengths of each square.