The length of a diagonal of a square is $6$. Then,its area is............

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is an altitude to the hypotenuse $AC$. If $AD = 9$ and $CD = 4$,find $BD$.

Hypotenuse of a right triangle is $25 \, cm$ and out of the remaining two sides,one is longer than the other by $5 \, cm$. Find the lengths of the other two sides.

In $\Delta PQR$,$M$ and $N$ are the midpoints of $\overline{PQ}$ and $\overline{PR}$ respectively. If the area of $\Delta PMN$ is $24$,find the area of $\Delta PQR$.

If $\Delta ABC \sim \Delta PQR$ under the correspondence $ABC \leftrightarrow QPR$,and given $m \angle A + m \angle B = 130^{\circ}$ and $m \angle B + m \angle C = 125^{\circ}$,find $m \angle Q$. (in $^{\circ}$)

In $\Delta ABC$,$\overline{AD}$ is a median and $AB^2 + AC^2 = 148$. If $AD = 7$,then $BC = \ldots$