In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $AB = 4$ and $BC = 7.5$,find $AC$.

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude. If $PQ = 40$ and $QR = 30$,find the area of $\Delta QMR$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. Then,$BM$ is the geometric mean of..............

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 18$,$AC = 14$,and $AD = 14$,find the perimeter of $\Delta ABC$.

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 $\Delta ABC$,the correspondences $ABC \leftrightarrow BAC$ and $ABC \leftrightarrow ACB$ are similarities. Then,$\Delta ABC$ is a/an $\ldots \ldots \ldots \ldots$ triangle.