To find TU, we can first find the length of EV by using the fact that E is the midpoint of TU. Since H is the midpoint of TV, we have HD = (1/2)TV.
If HD = 66, then (1/2)TV = 66.
Multiplying both sides of the equation by 2, we have TV = 132.
Since TV = 82 and TV = 132, we can set up a proportion to find the length of EU:
TV/EV = TV/UV
Rearranging the equation, we have TV * UV = TV * EV.
Plugging in the values we know, we get 132 * 66 = 82 * EV.
Dividing both sides of the equation by 82, we get (132 * 66) / 82 = EV.
Simplifying the right side of the equation, we have (8712) / 82 = EV.
Dividing the numerator by the denominator, we get EV = 106.
Since E is the midpoint of TU, we can double the length of EV to find TU: EV * 2 = 106 * 2 = 212.
Therefore, TU = 212.
To find TU - HD, we subtract the length of HD from TU: 212 - 66 = <<212-66=146>>146.
Therefore, TU - HD = 146.
Points E, D, and H are the midpoints of the sides of TUV, UV = 66, TV = 82, and HD = 66, Find TU -
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