I think it is BD perpendicular to AC.
so when BD is perpendicular to AC angle BDC = angle BDA = 90 degree.
Now taking triangle BDC, angle A=30 degrees(given) ; D =90(perpendicular).
Now, sum angle property gives angle B = 60. Therefore, it is a 30,60,90 triangle which gives us opposite sides to the angles as 1, root3, 2 respectively. so perimeter is given as 3+root3.
Now perpendicular BD divides AC into 2 equal parts. Therefore, DC=root3.
Also, in triangle BDC angle D=90 degree(perpendicular).
Now applying pythagoran theorem gives us BC=1+3=4.
Therefore, perimeter of triangle ABC gives us AB=2, AC=2root3, BC=4. Therefore perimeter ABC=6+2root3
THEREFORE (A) IS SUFFICIENT.
OPTION (B) IS INSUFFICIENT BECAUSE WE CAN'T FIND BC, WE CAN ONLY SAY DC=X/2.
SO ANSWER (A). LET ME KNOW IF I AM RIGHT.
