Answer:
y = 4.5
Step-by-step explanation:
Given that the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{AC}[/tex] = [tex]\frac{AE}{AD}[/tex]
Note that AD = AE + ED
Substituting relevant values into the ratios
[tex]\frac{3}{5\\}[/tex] = [tex]\frac{y}{3+y}[/tex] ( cross- multiply )
5y = 3(3 + y) ← distribute
5y = 9 + 3y ( subtract 3y from both sides )
2y = 9 ( divide both sides by 2 )
y = 4.5
