The length of UV is 6 in because it is parallel to WX.
Find the length of TV:
[tex]TV^{2} =\sqrt{TU^{2} +TV^{2}}[/tex]
[tex]TV^{2} =\sqrt{12^{2} +6^{2}}[/tex]
[tex]TV^{2} =\sqrt{144+36}[/tex]
[tex]TV^{2} =\sqrt{180}[/tex]
[tex]TV =6\sqrt{5} = 13.41640786[/tex]
The length of VX is 9 in because it is parallel to UW.
[tex]TX^{2} =\sqrt{TV^{2} +VX^{2}}[/tex]
[tex]TX^{2} =\sqrt{180 +9^{2}}[/tex]
[tex]TX^{2} =\sqrt{180 +81}[/tex]
[tex]TX^{2} =\sqrt{261}[/tex]
[tex]TX =16.15549442[/tex]
TX = 16.2 inches
