Triangles Questions

In $\Delta ABC$, $AD$ is the internal bisector of $\angle A$, meeting the side $BC$ at $D$. If $BD=5\text{cm}$ and $BC=7.5\text{cm}$, then the ratio $AB:AC$ is:

Two circles with centers $B$ and $D$ have radii $DA=8\text{cm}$ and $BC=x\text{cm}$, respectively. $AC$ is tangent to both circles. If $DB$ and $AC$ intersect at the point $E$, $AE=12\text{cm}$ and $EC=18\text{cm}$, then find the value of $x$ (in $\text{cm}$).

If $L$ is the mid-point of the side $YZ$ of $△XYZ$, and the area of $△XYL$ is $13{\text{cm}}^2$, then the area (in ${\text{cm}}^2$) of $△XYZ$ is: