Final answer:
The problem presented cannot be solved due to insufficient and conflicting information regarding the relationship between ΔHED and ΔTUV and the missing details needed to connect sides HD, UV, and TV.
Step-by-step explanation:
The question provided contains insufficient information to solve the problem as there are typos and misleading information regarding triangle ΔHED and triangle ΔTUV. It is mentioned that points E, D, and H are midpoints of the sides of ΔHED which is self-referential, and the problem asks to find the perimeter of ΔTUV with given lengths UV = 68, TV = 86, and HD = 54. However, there is no indication of how HD relates to triangle TUV. Without a clear relationship between these elements or additional information, it is impossible to determine the correct perimeter of triangle TUV. The problem as stated cannot be solved, and therefore, a definitive answer to the question cannot be provided.