A wire is cut into two pieces, one of length \(a\) and the other of length \(b\). The piece of length \(a\) is bent to form an equilateral triangle, and the piece of length \(b\) is bent to form a regular hexagon. The triangle and the hexagon have equal area. The original answer is in the form \(\frac{\sqrt{p}}{n}\) where the fraction is in its simplest form. Please give the value of \(p + n\).

Let's think step by step and output the final answer within \boxed{}.
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