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 $AB = 6$ and $AC = 10$,find the area of $\Delta ABC$.

$A$ girl of height $90\, cm$ is walking away from the base of a lamp-post at a speed of $1.2\, m/s$. If the lamp is $3.6\, m$ above the ground,find the length of her shadow after $4\, seconds$.

In $\Delta ABC$,$\overline{AB} \cong \overline{AC}$ and $\overline{AD}$ is a median. If $BC = 12$ and $AD = 8$,find $AB$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 5.2$,$AC = 10.4$,and $BD = 3.8$,find $BC$.

In rhombus $ABCD$,$AC = 16$ and $BD = 30$. Find its perimeter.