Hello people, here is my question

∠AEB  ≅  ∠CED   because they are vertical angles

∠EAB  ≅  ∠ECD   because they are alternate interior angles

So by the AA similarity theorem, △EAB ~ △ECD

Since △EAB ~ △ECD,

CD / AB  =  DE / BE

100 / 150  =  DE / BE

2 / 3  =  DE / BE

∠BCD  ≅  ∠BFE   because they are corresponding angles

∠BDC  ≅  ∠BEF   because they are corresponding angles

So by the AA similarity theorem, △BCD ~ △BFE

Since △BCD ~ △BFE,

DC / EF  =  BD / BE                       And    DC  = 100     and     BD  =  BE + DE

100 / EF  =  (BE + DE) / BE           Distribute  1 / BE  to the terms in parenthesees.

100 / EF  =  BE / BE + DE / BE

100 / EF  =  1 + DE / BE                And  DE / BE  =  2 / 3

100 / EF  =  1 + 2 / 3

100 / EF  =  5 / 3                Multiply both sides of the equation by  3 .

300 / EF  =  5                     Multiply both sides of the equation by  EF .

300  =  5 * EF                    Divide both sides of the equation by  5 .

60  =  EF

The number of centimeters in the length of EF is  60 .

Thank you hectictar