$A$ vertical pole of length $6\, m$ casts a shadow $4\, m$ long on the ground and at the same time a tower casts a shadow $28\, m$ long. Find the height of the tower. (in $m$)

If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$,and the perimeter of $\Delta ABC$ is $48$ while the perimeter of $\Delta PQR$ is $60$,find the ratios $\frac{AB}{PQ}$ and $\frac{AB + BC}{PQ + QR}$.

It is given that $\triangle FED \sim \triangle STU$. Is it true to say that $\frac{DE}{ST} = \frac{EF}{TU}$? Why?

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$. If $AB : PQ = 3 : 4$ and the perimeter of $\Delta PQR$ is $24$,find the perimeter of $\Delta ABC$.

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle P$ and $\angle B \cong \angle Q$. If $\frac{AB}{PQ} = \frac{4}{5}$ and $AC = 20$,find $PR$.

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XZY$. If $PQ = 8$,$XZ = 12$ and the area of $\Delta PQR$ is $24$,find the area of $\Delta XYZ$.