we know that
triangles BCD and ACE are similar
so, their ratios of sides must be equal
Calculation of y:
[tex]\frac{BC}{AC}=\frac{CD}{CE}[/tex]
we can see that
AC=AB+BC
AC=y+3
CE=CD+DE
CE=4+6
CE=10
now, we can plug values
[tex]\frac{3}{y+3}=\frac{4}{10}[/tex]
now, we can solve for y
[tex]3*10=4*(y+3)[/tex]
[tex]30=4y+12[/tex]
[tex]30-12=4y+12-12[/tex]
[tex]18=4y[/tex]
[tex]y=4.5[/tex]
Calculation of AC:
we know that
AC=y+3
we can plug y
and we get
[tex]AC=4.5+3[/tex]
[tex]AC=7.5[/tex]...................Answer
