Final answer:
Since ZE is a perpendicular bisector and the triangle is equilateral, BC is twice the length of ZE, which results in BC being 102.
Step-by-step explanation:
To find BC, which is the side of triangle AABC, we need to use the fact that ZD, ZE, and ZF are perpendicular bisectors of the triangle. Since ZE = 51, and it is a perpendicular bisector, then EB = EC = 51. Given that the sides AB = BC = CA, we know that the triangle is equilateral. Hence, each side of the triangle is twice the length of ZE, which is 51.
Therefore, BC = 2 × ZE = 2 × 51 = 102.