Answer:
y = [tex]\frac{4}{3}[/tex]
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{BE}{CD}[/tex], substituting values
[tex]\frac{2}{y-2}[/tex] = [tex]\frac{5}{y-3}[/tex] ( cross- multiply )
5(y - 2) = 2(y - 3) ← distribute both sides
5y - 10 = 2y - 6 ( subtract 2y from both sides )
3y - 10 = - 6 ( add 10 to both sides )
3y = 4 ( divide both sides by 3 )
y = [tex]\frac{4}{3}[/tex]
