In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YP}$ is a median. If $YP = 6$,then $XZ = \ldots$

In $\Delta ABC$,$m \angle A = 90^{\circ}$,$AB = 8$ and $AC = 15$. Then,$BC = \ldots$.

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow QRP$. If $m \angle A = 80^{\circ}, m \angle B = 40^{\circ}$ and $m \angle C = 60^{\circ}$,find the measures of all the angles of $\Delta PQR$.

In $\Delta ABC$,$m \angle A = 90^{\circ}$. If $a = 20$ and $b = 12$,then $c = \dots$

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 2x$,$BM = 3x + 5$,and $CM = 8x$,find the value of $x$.

When a ladder leans on a wall to reach a height of $8 \, m$, its lower end rests $6 \, m$ away from the base of the wall. If the same ladder leans on the wall to reach a height of $6 \, m$, find the distance of its lower end from the base of the wall. (in $m$)