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Thus, the original radius is \(\boxed{\frac{3 + \sqrt{141}}{3}}\).
A wind turbine blade is designed as a sector of a circle with radius 15 meters and central angle \(120^\circ\). Find the perimeter of the blade, including the two straight edges and the curved arc.
The perimeter of the blade includes two radii and the arc length. The arc subtends \(120^\circ\), which is \(\frac{120}{360} = \frac{1}{3}\) of a full circle.

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