Answer:
BD = 8
Step-by-step explanation:
You want the length of altitude BD in right triangle ABC if AD=DC=8.
The fact that altitude BD intersects AC at its midpoint means all of the triangles are isosceles. The legs of the smaller right triangles in this geometry are all the same length: 8 units.
BD = 8
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Additional comment
The altitude can also be found from the geometric mean relation ...
BD = √(AD·DC) = √(8·8) = 8
This relation comes from the fact that the triangles are all similar:
BD/AD = DC/BD