Finding triangle area but something wrong

[wiwatmongkonthan]

My method is too easy. Maybe wrong.

 

[wiwatmongkonthan]

156 is wrong because this case
area of triangle DEF is 144 square root 4

 

[wiwatmongkonthan]

Sorry it is 144 square root 3

 

[lev888]

1. The question is "what is the maximum perimeter". Your solution does not consider that there are multiple possible values for the perimeter.
2. Why do you think that FE is parallel to BC? If you are considering this special case separately, you must also consider all cases where FE is not parallel to BC.

 

[wiwatmongkonthan]

I try 2-3 cases but not work.
Please suggest me.