Answer
$DE=5$
Work Step by Step
To find the length of the segment DE, we use the relationship between similar polygons.
$\frac{DE}{BC}=\frac{AD}{AB}$
Where
$BC = 10$
$AD=6$
$AB=AD+DB=6+6=12$
So, solving for DE gives:
$DE=\frac{AD}{AB}*BC=\frac{6*10}{12}=5$
