If in two triangles $ABC$ and $PQR$,$\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}$,then

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = x$,$MB = x-2$,$AN = x+2$ and $NC = x-1$,find the value of $x$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BE}$ is a median. If $AB = 15$ and $BE = 8.5$,find $BC$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $BM = 12$ and $CM = 18$,find $AB$.

$\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EFD$. If $XY : EF = 2 : 3$ and the area of $\Delta XYZ$ is $18$,then the area of $\Delta DEF$ is........

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 $, km$)?