If we know the difference in their areas, how big are these sectors?

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The figure shows two sectors in which \(AB\), \(CD\) are arcs of concentric circles, centre \(O\) and radii \(\quantity{2k}{cm}\) and \(\quantity{3k}{cm}\) respectively. \(A\hat{O}B\) is \(\frac{3}{4}\) radian and the area \(ABDC\) is \(\quantity{30}{cm^2}\). Find

1. the value of \(k\),
2. the difference between the lengths of the arcs \(AB\) and \(CD\).