In $\Delta XYZ$,$A$ and $B$ are the midpoints of $XY$ and $XZ$ respectively. If $AB = 7.5 \, cm$,then find the length of $YZ$ in $cm$.

State whether each of the following statements is true or false:
$(1)$ $ABCD$ is a rhombus. If $AB = 12 \, \text{cm}$, then the perimeter of $ABCD$ is $48 \, \text{cm}$.
$(2)$ $PQRS$ is a square. If $PR = 8 \, \text{cm}$, then the perimeter of $PQRS$ is $32 \, \text{cm}$.

In parallelogram $ABCD$,the diagonals intersect at $P$. If $PA = 3.8 \, cm$ and $PB = 5.2 \, cm$,then $BD = \dots \dots \dots cm$.

In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $PQ + BC = 8.4 \, cm$ and $AB + AC = 20.5 \, cm$,then find the perimeter of $\Delta ABC$ in $cm$.

Three angles of a quadrilateral are $75^{\circ}, 90^{\circ}$ and $75^{\circ}$. The fourth angle is (in $^{\circ}$)

In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $BC = 8.2 \text{ cm}$,then $PQ = \dots \text{ cm}$.