Given $\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$. If $AB : XY = 4 : 5$ and $YZ = 20$,find $BC$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $AB : AC = 24 : 25$. If $BC = 14$,find the perimeter of $\Delta ABC$.

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

$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow ZYX$. If $AB = 3, BC = 5, CA = 6$ and $XY = 6$,find the perimeter of $\Delta XYZ$. (in $.8$)

As shown in the adjoining diagram of a staircase,the width of each step is $20 \, cm$ and the height is $15 \, cm$. Find the distance between points $A$ and $B$ in meters.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is a median. If $m \angle C = 30^{\circ}$ and $AB = 5$,find $BD$.