The figure shows a rectangle \(ABCD\) with \(AD=15\text{ cm}\). \(E\) is on \(DC\) produced such that \(DE=8\text{ cm}\). The area of the shaded part \(X\) is \(12\text{ cm}^2\) more than the area of the shaded part \(Y\). Find the length of \(AB\).[3]
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