Answer:
EC = 3.75
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{AC}{AE}[/tex] = [tex]\frac{BC}{DE}[/tex] , substitute values
[tex]\frac{AC}{5}[/tex] = [tex]\frac{1}{4}[/tex] ( cross- multiply )
4 AC = 5 ( divide both sides by 4 )
AC = 1.25
Then
EC = AE - AC = 5 - 1.25 = 3.75
