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:

According to the Angle Bisector Theorem in a triangle, the internal bisector of an angle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Therefore, for $\Delta ABC$ with angle bisector $AD$:

$$\frac{AB}{AC}=\frac{BD}{DC}$$

We are given:

* $BD=5\text{cm}$
* $BC=7.5\text{cm}$

First, find the length of segment $DC$:

$$DC=BC-BD$$

$$DC=7.5\text{cm}-5\text{cm}=2.5\text{cm}$$

Now, substitute the values of $BD$ and $DC$ into the ratio:

$$\frac{AB}{AC}=\frac{5}{2.5}$$

$$\frac{AB}{AC}=\frac{2}{1}$$

Thus, the ratio $AB:AC=2:1$.