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 $\overline{AC}$. If $AM = 12$ and $CM = 3$,then $BM = \dots$

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is a median. If $AB = 15$ and $BM = 12.5$,find $BC$.

In $\Delta ABC$,$AB = AC = 37$,$BC = 70$ and $\overline{AM}$ is a median. Find $AM$.

An aeroplane leaves an airport and flies due North at $300 \, km/h$. At the same time,another aeroplane leaves the same airport and flies due West at $400 \, km/h$. How far apart will the two aeroplanes be after $1 \frac{1}{2}$ hours (in $, km$)?

In $\Delta ABC$ and $\Delta PQR$,$m \angle A = 30^{\circ}$,$m \angle C = 60^{\circ}$,$m \angle P = 90^{\circ}$ and $m \angle Q = 30^{\circ}$. Then,the correspondence $ABC \leftrightarrow \ldots$ is a similarity.