In the triangles below, $\displaystyle{m}\angle{T}={m}\angle{W}\usepackage{cmbright}\Huge\$ and $\displaystyle{m}\angle{U}={m}\angle{X}\usepackage{cmbright}\Huge\$ .

The length of $\displaystyle{\overline{{{X}{Y}}}}\usepackage{cmbright}\Huge\$ is _____.