Answer
$YZ = 10/\sqrt 2$ = 7.07
$XY= 10/\sqrt 2$ = 7.07
Work Step by Step
By the given Figure
$\angle Z=90^{\circ}$ given
$\angle X=45^{\circ}$ given
So remaining$ \angle Y=45^{\circ}$
now XY= 10 given
$YZ = 10/\sqrt 2$ = 7.07
$XY= 10/\sqrt 2$ = 7.07
By Theorem 5.5.1/ (45-45-90 Theorem)