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.

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

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.