The perimeter of equilateral $\Delta ABC$ is $30$. Find its area. (in $\sqrt{3}$)

If the measures of the sides of a triangle are $\ldots \ldots \ldots,$ then it is not a right-angled triangle.

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $YM = 12$ and $XM = 8$,find $XZ$.

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle Q$ and $\angle B \cong \angle R$. Which correspondence between them is a similarity?

$A$ $15 \, m$ 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 rectangle $ABCD$,$AB = 9$ and $BC = 12$. Then,$BD = \ldots$