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3 October, 17:27

Given that UT is the perpendicular bisector of AB, where T is on AB, find the length of AT given AT = 3x + 6 and TB = 42 - x.

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  1. 3 October, 17:28
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    make at equal to tb. solve for x, then plug the answer you got for x into the equation 3x plus 6, and the answer you get is the length of at
  2. 3 October, 17:30
    0
    A perpendicular bisector cuts the segment into two equal pieces. We're told that T bisects AB, and UT is the perpendicular bisector.

    So, AT = TB.

    We're told that AT = 3x + 6 and TB = 42 - x. We set them equal to each other, find x, and report the length.

    3x + 6 = 42 - x

    4x + 6 = 42

    4x = 36

    x = 9

    So AT's length is 3 * 9 + 6 = 27 + 6 = 33. TB's length is 33 too.
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