Question Number 182336 by Shrinava last updated on 07/Dec/22
Answered by mr W last updated on 08/Dec/22
Commented by Acem last updated on 08/Dec/22
$${Your}\:{old}\:{and}\:{simpler}\:{method}\:{was}\:{also}\:{clear} \\ $$$$\:{because}\:{AB}//\:{the}\:{base}, \\ $$$$\:{hence}\:{it}\:{has}\:\mathrm{2}\:{angles}\:{of}\:\mathrm{60}\:{so}\:{it}'{s}\:{equilateral}\:{too} \\ $$$$\:{or}\:{isoscelles}\:{in}\:{general}\:{case}\:{with}\:{angle}\:{of}\:\mathrm{2}\alpha \\ $$
Commented by mr W last updated on 08/Dec/22
$${EC}={DC}={x} \\ $$$$\Delta{ABE}\sim\Delta{DCE} \\ $$$$\Rightarrow{EB}={AB}=\mathrm{6} \\ $$$${EC}=\mathrm{6}+\mathrm{8}=\mathrm{14}={x} \\ $$
Commented by mr W last updated on 08/Dec/22
$${i}\:{didn}'{t}\:{change}\:{my}\:{method}\:{at}\:{all}.\: \\ $$$${i}\:{just}\:{added}\:{some}\:{intermediate}\:{steps}. \\ $$
Commented by SEKRET last updated on 08/Dec/22
$$\boldsymbol{\mathrm{beatiful}}\:\boldsymbol{\mathrm{solution}} \\ $$