Final answer:
The length of HE is 59.
Step-by-step explanation:
Given that E, D, and H are the midpoints of the sides of triangle TUV and that UV = 118, TV = 144, and HD = 118, we can use the Midsegment Theorem to find the length of HE.
The Midsegment Theorem states that the length of the midsegment is equal to half the length of the side it is parallel to. Since HD is parallel to UV, we can use the theorem to find the length of HE.
HD = 118, so HE = HD/2 = 118/2 = 59. Therefore, the length of HE is 59, which corresponds to option (d).