Answer:
10√6
Step-by-step explanation:
You want the altitude BD in right triangle ABC, where it divides hypotenuse AC into the parts AD=20 and DC=30.
The right triangles in the figure are all similar, so we have ...
[tex]\dfrac{BD}{AD}=\dfrac{DC}{BD}\\\\BD=\sqrt{AD\cdot DC}=\sqrt{20\cdot30}\\\\\boxed{BD=10\sqrt{6}}[/tex]