The lengths of the diagonals of a rhombus are $16 \, cm$ and $12 \, cm$. Then,the length of the side of the rhombus is (in $cm$)

$A$ $4 \,m$ long ladder leans on a wall to reach a height of $3.2 \,m$ on the wall. Find the distance in $m$ between the lower end of the ladder and the base of the wall.

$\square PQRS$ is a rectangle. $PQ + QR = 7$ and the area of $\square PQRS$ is $12$. Then,$PR = \ldots$

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 $m$)

The correspondence $PQR \leftrightarrow ZYX$ between $\Delta PQR$ and $\Delta XYZ$ is a similarity. If $PQ : ZY = 5 : 3$ and $PR = 10$,find $ZX$.

In $\Delta ABC$,$m\angle B = 90^\circ$. If $AB = 12$ and $BC = 5$,then $AC = \dots$