In $\Delta ABC$,$AB = 4$,$BC = 2\sqrt{3}$,and $AC = 2\sqrt{7}$. Then,in $\Delta ABC$,the length of the median on the longest side is $\ldots$

In $\Delta XYZ$,$\overline{XM}$ is a median. If $XY = 11$ and $XM = YM = 30.5$,find $XZ$.

Nazima is fly fishing in a stream. The tip of her fishing rod is $1.8 \, m$ above the surface of the water and the fly at the end of the string rests on the water $2.4 \, m$ away from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut,how much string does she have out? If she pulls in the string at the rate of $5 \, cm$ per second,what will be the horizontal distance of the fly from her after $12 \, seconds$?

State whether the following statement is true or false. Justify your answer.
$\triangle ABC$ with vertices $A(-2, 0), B(2, 0)$ and $C(0, 2)$ is similar to $\triangle DEF$ with vertices $D(-4, 0), E(4, 0)$ and $F(0, 4)$.

The perimeter of square $ABCD$ is $48$. Find the length of its diagonal $\overline{AC}$. (in $\sqrt{2}$)

In $\Delta XYZ$,$m\angle X = 90^{\circ}$,$XY = 8$ and $YZ = 17$. Then,the area of $\Delta XYZ$ is.............