Question: Triangle ABC has side AB = AC = 10 and BC = 12. The center of square DEFG is at the centroid of triangle ABC,

Triangle ABC has side AB = AC = 10 and BC = 12. The center of square DEFG is at the centroid of triangle ABC, and vertices D and E lie on side BC of the triangle. The perimeter of the region of points both inside the triangle and inside the square can be written as (m/n), where m and n are relatively prime positive integers. Find m + n.

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