Dissecting Triangles

The centroid is the point of concurrency of the medians of a triangle. In the given diagram, $P$ is the centroid.

Using the Centroid Theorem, we can write an equation that we can use to find the desired length $AP.$ $$\begin{array}{c}AP=\frac{2}{3}AD\end{array}$$ Knowing that $AD=30,$ we can substitute it in the equation above to find $AP.$