We are given a triangle and told that line WY is a perpendicular bisector to side XZ. This line basically splits the triangle into two triangles: XYW and YZW.
Note that as both triangles have two pairs of sides with the same length and a congruent angle (angles XWY and YWZ are both 90°), both triangles are congruent. THat is, corresponding sides have the same length.
This leads to having sides XY and YZ to be congruent. So we have the equation
[tex]12x\text{ -5=129}[/tex]
first, we add 5 on both sides. So we get
[tex]12x=129+5=134[/tex]
Finally, we divide both sides by 12. We get
[tex]x=\frac{134}{12}[/tex]
Note that
[tex]x=\frac{132+2}{12}=\frac{132}{12}+\frac{2}{12}=11+\frac{1}{6}[/tex]
so we have that
[tex]x=11\frac{1}{6}[/tex]
