In triangle \(ABC\), \(AB = 7\) units, \(BC = 24\) units, and \(CA = 25\) units. A rectangle \(PQRS\) has the same perimeter as triangle \(ABC\). If the width of the rectangle is 8 units, what is the area of the square that has the same perimeter as the rectangle? Let's think step by step and output the final answer within \boxed{}.
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