In the triangle ABC, it is known that sina + sinc = 2sinb, and B = 60 degrees. If the area of triangle ABC is [root 3 / 2], then the opposite side B of angle B is equal to

In the triangle ABC, it is known that sina + sinc = 2sinb, and B = 60 degrees. If the area of triangle ABC is [root 3 / 2], then the opposite side B of angle B is equal to

sinA+sinC=2sinB
According to the sine theorem
a+c=2b
a²+c²+2ac=4b²
The area of triangle ABC is [root 3 / 2]
S△=1/2acsinB
√3/2=1/2acsin60°
ac=2
a²+c²=4b² -4
According to the cosine theorem
b²=a²+c²-2accosB
b²=4b² -4-2
3b²=6
b=√2