In $\Delta ABC$,$m\angle B = 90^{\circ}$. If $a = 16$ and $c = 12$,then $b = \ldots$

The heights of two poles standing erect on a flat ground are $6 \, m$ and $11 \, m$. If the distance between their bases is $12 \, m$,find the distance between their tops.

Below are given the measures of sides $\overline{PQ}$,$\overline{QR}$ and $\overline{PR}$ of $\Delta PQR$. In each case,determine whether $\Delta PQR$ is a right-angled triangle or not. If it is a right-angled triangle,state which angle is a right angle: $PQ = 8, QR = 6, PR = 12$.

In $\Delta PQR,$ $\overline{PS}$ is a median. If $PQ = 12$ and $PS = QS = 18.5,$ find $PR$.

$\Delta XYZ \sim \Delta ABC$ for the correspondence $XYZ \leftrightarrow ABC$. If $\frac{XY}{AB} = \frac{3}{5}$,then $\frac{BC}{YZ} = \dots$

As shown in the adjoining diagram,$\angle B$ is an obtuse angle and $\overline{AM}$ is an altitude in $\Delta ABC$. Prove that $AC^{2} = AB^{2} + BC^{2} + 2 \cdot BC \cdot BM$.