Question 1181299
If   {{{AD/DB =3/4}}} and  {{{DE}}} || {{{BC}}}

by proportionality theorem, we have

{{{AD/DB=AE/EC}}} ........... substitute {{{AD/DB =3/4}}}, and add  {{{1}}} to both sides we have

{{{3/4+1=AE/EC+1}}}

{{{7/4=(AE+EC)/EC }}}

{{{7/4=AC/EC}}} ........substitute{{{ AC =15}}}  

{{{7/4=15/EC}}}........cross multiply

{{{7EC=15*4}}}

{{{7EC=60}}}

{{{EC=60/7}}}

{{{EC=8.6}}}


now find {{{AE}}}

{{{AC=AE+EC}}}

{{{15=AE+8.6}}}

{{{15-8.6=AE}}}

{{{AE=6.4}}}