$\square ABCD$ is a square. If its perimeter is $40$, find $AC + BD$. (in $\sqrt{2}$)

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$. If $XY = a^{2} - b^{2}$ and $YZ = 2ab$,find $XZ$ (where $a > b > 0$).

In a square,the length of a diagonal is $8$. Find the length of the sides of the square. (in $\sqrt{2}$)

In $\Delta XYZ$,the bisector of $\angle X$ intersects $\overline{YZ}$ at $M$. If $XY = 3.6$,$XZ = 4.2$ and $MZ = 2.8$,find $YM$.

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 8$,$BC = 18$,and $AD = 7$,then $AC = \ldots$

In $\Delta XYZ$,$X-S-Y$,$X-T-Z$ and $\overline{ST} \parallel \overline{YZ}$. If $XS = 4$,$XT = 8$,$SY = x-4$ and $TZ = 3x-19$,find the value of $x$.