Question 1193614
△CDE ~ △CBA with ∠CDE ≅ ∠B.

If {{{CD = 10}}}, {{{CA = 18}}}, and {{{EB = 11}}}, find{{{ CE}}}.


similar triangles have proportional corresponding sides 


{{{CD/CB = CE/CA}}}


Since {{{CD = 10}}} , {{{CA = 18}}} , {{{CB = CE + EB}}} , {{{EB = 11}}}, then {{{CB = CE + 11}}} :


{{{10/(CE + 11) = CE/18}}}


cross-multiplying:


{{{ 10 *18=CE(CE + 11)}}}


{{{CE^2 +11CE - 180 = 0}}}

{{{(CE + 20)(CE - 9) = 0}}}

  {{{CE = -20}}} or {{{CE = 9}}}

disregard negative solution for the length

so,  {{{CE = 9}}}