Let the length of shortest side be x cm.
According to the given information,
Longest side = 2 x Shortest side = 2x cm
And third side = 2 + Shortest side = (2 + x) cm
Perimeter of triangle = x + 2x + (x + 2) = 4x + 2
But it is given that,
Perimeter > 166 cm
=> 4x + 2 > 166 => 4x> 166-2 => 4x>164
x>164/4 =41 cm
Hence, the minimum length of shortest side is 41 cm.