Question 1205859
{{{ drawing( 600, 600, -10, 10, -10, 10,

blue(line(0,0,2,8)), blue(line(0,0.1,9,0.1)), blue(line(2,8,9,0.1)), 
green(line(1,5,5,5)), locate(2,8.5,A),locate(0.1,-0.5,B),locate(9,-0.5,C),
locate(0.5,5,D),locate(5,5,E),locate(1,6,9),locate(.2,3,18),locate(3.5,7,12),
locate(2,5,10),locate(7,3,y),locate(5,0.65,x),
graph( 600, 600, -10, 10, -10, 10, 0)) }}} 


GIVEN: 

{{{AD = 9}}}
{{{ AE = 12}}}
{{{DE = 10}}}
{{{DB = 18}}}

triangle {{{ABC}}} is similar to triangle {{{DEA}}}, and similar triangles have proportional corresponding side lengths

{{{AB=AD+BD = 9+18=27}}}
{{{AC=12+y}}}
then

{{{AD/AB=10/x}}}

{{{9/27=10/x}}}

{{{9x=270}}}

{{{x=30}}}


and

{{{AD/AB=12/(12+y)}}}

{{{9/27=12/(12+y)}}}

{{{9(12+y)=12*27}}}

{{{9(12+y)=(12*27)/9}}}

{{{12+y=12*3}}}

{{{12+y=36}}}

{{{y=36-12}}}

{{{y=24}}}

answer:

{{{BC=30}}}
{{{CE=24}}}
{{{AC=12+24=36}}}