Verticality refers to dividing triangle ABC into two right-angled triangles. In other words, the sum of squares of two short sides of a right triangle is equal to the square of the long side.

So AD*AD+BD*BD=AB*AB.

AD*AD+DC*DC=AC*AC

So DB= root number 12 and DC= root number 3, so BC=BD+DC= root number 12+ root number 3.