Given the picture, what is the length of AC? A) 4.5 B) 5 C) 7.5 D) 8

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+BCAC=y+3CE=CD+DECE=4+6CE=10now, 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+3we can plug y and we get [tex]AC=4.5+3[/tex][tex]AC=7.5[/tex]...................Answer