In $\Delta XYZ$,$X-P-Y$,$X-Q-Z$ and $\overline{PQ} \parallel \overline{YZ}$. If $XP:PY = 3:5$ and $XZ = 5.6$,find $QZ$.

In $\Delta ABC$,$m \angle C = 90^\circ$,$AB = 12.5$ and $BC = 12$. Find $AC$.

$ABCD$ is a trapezium in which $AB \parallel DC$ and $P$ and $Q$ are points on $AD$ and $BC$ respectively such that $PQ \parallel DC$. If $PD = 18 \, cm$,$BQ = 35 \, cm$ and $QC = 15 \, cm$,find $AD$ (in $cm$).

In $\Delta ABC$,$m \angle A = 90^\circ$. If $b = 12$ and $c = 35$,then $a = \ldots$

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle P$ and $\angle B \cong \angle R$. If $AB = 8$,$PQ = 7.5$ and $AC = 6$,find $PR$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM : MB = 4 : 13$ and $AC = 20.4$,find $AN$.