In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BE}$ is a median. If $AB = 3.6$ and $BC = 4.8$,find $BE$.

$A$ $2.6 \,m$ long ladder leans on a wall such that its lower end remains $1 \,m$ away from the base of the wall. Then,its upper end reaches to the height of .....$m$ on the wall.

$A$ ladder is placed leaning on a wall. Its upper end reaches to the height of $12 \, m$ on the wall and its lower end rests $9 \, m$ away from the base of the wall. Find the length of the ladder in meters.

In rhombus $ABCD$,$AB = 13$ and $AC = 24$. Find $BD$.

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow QPR.$ If $m \angle P : m \angle Q : m \angle R = 2 : 3 : 4,$ then $m \angle A : m \angle B : m \angle C = \ldots$

In $\Delta ABC$,$A-D-B$,$A-E-C$ and $BD = CE$. If $m\angle B = m\angle C$,prove that $\overline{DE} \parallel \overline{BC}$.