Question

How do I solve for h

Answer 1

All the triangles are similar, so the ratio of (long leg)/(short leg) is the same. The long leg of ΔADB is
.. AD = AC -DC = 20 -4
.. AD = 16

Then
.. (long leg)/(short leg) = AD/DB = BD/DC
.. 16/h = h/4
.. h^2 = 64
.. h = 8

Selection D is appropriate.

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You may see this again. The altitude (h) from the right angle in a right triangle is the geometric mean of segments AD and DC. That is,
.. h = √((AD)*(DC))