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

In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $AC - BC = 4$ and $BC - AB = 4$,find the lengths of all the sides of $\Delta ABC$.

In $\Delta ABC$ and $\Delta XYZ$,$\frac{AB}{XY} = \frac{BC}{YZ}$ and $\angle B \cong \angle Y$. If $AB = 6$,$AC = 15$,and $XY = 15$,find $XZ$.

Corresponding sides of two similar triangles are in the ratio of $2:3$. If the area of the smaller triangle is $48 \, cm^2$,find the area of the larger triangle (in $cm^2$).

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 12$ and $CM = 3$,find $BM$.

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