Answer
10
Work Step by Step
The two triangles are similar. Thus, we can write the following proportion:
$$ \frac{5\sqrt3}{BC}=\frac{5}{5\sqrt3} \\ 5BC=25\cdot 3 \\ BC=15$$
So, the length of BD is:
$$ =15-5 \\ =10$$
Elementary Geometry for College Students (7th Edition)
by Alexander, Daniel C.; Koeberlein, Geralyn M.
Published by
Cengage
ISBN 10:
978-1-337-61408-5
ISBN 13:
978-1-33761-408-5
Chapter 5 - Section 5.6 - Segments Divided Proportionally - Exercises - Page 269: 37
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