DC = [tex]\frac{5}{2}[/tex] = 2.5
since the triangles are similar then the ratios of corresponding sides are equal
[tex]\frac{AC}{AD}[/tex] = [tex]\frac{BC}{DE}[/tex]
[tex]\frac{7.5+DC}{7.5}[/tex] = [tex]\frac{8}{6}[/tex] (cross-multiply )
45 + 6DC = 60
6DC = 60 - 45 = 15 ( divide both sides by 6 )
DC = [tex]\frac{5}{2}[/tex]
