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\includegraphics[max width=\textwidth, alt={}, center]{11bfe5bd-604c-43e5-81e7-4c1f5676bcbb-2_485_755_751_696} The diagram shows a plan for a rectangular park \(A B C D\), in which \(A B = 40 \mathrm {~m}\) and \(A D = 60 \mathrm {~m}\). Points \(X\) and \(Y\) lie on \(B C\) and \(C D\) respectively and \(A X , X Y\) and \(Y A\) are paths that surround a triangular playground. The length of \(D Y\) is \(x \mathrm {~m}\) and the length of \(X C\) is \(2 x \mathrm {~m}\).

1. Show that the area, \(A \mathrm {~m} ^ { 2 }\), of the playground is given by $$A = x ^ { 2 } - 30 x + 1200$$
2. Given that \(x\) can vary, find the minimum area of the playground.