Properties of Triangles

In a $\triangle A E X, T$ is the mid-point of $X E$ and $P$ is the mid-point of $E T$. If the $\triangle A P E$ is equilateral of side length equal to unity, then which of the following alternative is not correct?

In a triangle $A B C$ as shown in the diagram, where $A B=5, A C=10$ and $B D=1$, then perimeter of $\triangle A B C$ is