Answer
a)
$AD=4\sqrt {3}$
b)
$BD=4.5$
Work Step by Step
a)
$\frac{AD}{BD}=\frac{DC}{AD}$
$\frac{AD}{6}=\frac{8}{AD}$
$AD^{2}=8\times6$
$AD^{2}=48$
$AD=\sqrt {48}$
$AD=4\sqrt {3}$
b)
$\frac{AD}{BD}=\frac{DC}{AD}$
$\frac{6}{BD}=\frac{8}{6}$
$6\times6=8BD$
$36=8BD$
$BD=\frac{9}{2}=4.5$
