Points E, D, and H are the midpoints of the sides of TUV.UV=100, TV=120, and HD=100.
FIND TU
In triangle TUV, the midpoints of the sides divide the triangle into four equal smaller triangles: TUE, UVE, VTH, and HTU.
Since HD is a midline of triangle TUV, its length is equal to half the length of TV. Therefore, HD = 120/2 = 60.
Since D is the midpoint of UV, UD = DV = UV/2 = 100/2 = 50.
Using the Pythagorean theorem in triangle HUD, we can find the length of TU:
TU^2 = TH^2 + UD^2
TU^2 = 100^2 + 50^2
TU^2 = 10000 + 2500
TU^2 = 12500
TU = √12500
TU ≈ 111.8
Therefore, the length of TU is approximately 111.8.