In $\Delta ABC$,$D$ is the midpoint of $\overline{BC}$,$AB = 7$,$AC = 5$ and $AD = 5$. Then $BC = \ldots$

In $\Delta ABC$,$\overline{AB} \cong \overline{AC}$ and $\overline{AD}$ is a median. If $AD = 12$ and the perimeter of $\Delta ABC$ is $36$,find the area of $\Delta ABC$.

In $\Delta ABC$,$\angle B$ is a right angle. Then,according to Pythagoras' theorem,$\ldots \ldots \ldots$ holds good.

$A$ $15 \, m$ long bamboo leans on a wall to reach the height of $12 \, m$ on the wall. Then,the lower end of the bamboo is $\ldots \ldots \, m$ away from the base of the wall.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is an altitude to the hypotenuse $AC$. If $AD = 9$ and $CD = 27$,find $AB$.

In the given figure,if $\angle D = \angle C$,then is it true that $\triangle ADE \sim \triangle ACB$? Why?