In $\Delta ABC$,$\overline{AD}$ is a median. If $AD = 7$ and $AB^2 + AC^2 = 148$,find $BC$.

In $\Delta ABC$,$AB = 3$,$BC = 6$,and $AC = 8$. In $\Delta PQR$,$PQ = 13.6$,$QR = 10.2$,and $PR = 5.1$. Which correspondence between $\Delta ABC$ and $\Delta PQR$ is a similarity?

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QD}$ is an altitude. If $PD = 9 DR$,then $PQ = \ldots \ldots \ldots \times QR$.

In $\Delta ABC$,$m \angle A + m \angle B = m \angle C$. If $AC : BC = 3 : 4$ and $AB = 17.5$,find the perimeter of $\Delta ABC$.

Given $\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$. If $AB : XY = 4 : 5$ and $YZ = 20$,find $BC$.

In $\Delta XYZ$,$X-S-Y$,$X-T-Z$ and $\overline{ST} \parallel \overline{YZ}$. If $XS = 4$,$SY = 4.5$ and $XT = 8$,find $XZ$.