Since each point of the triangle is going to be 1.5 times as far from the center of dilation, each side will increase by a factor of 1.5..
3 x 1.5 = 4.5m
4 x 1.5 = 6m
5 x 1.5 = 7.5m
So the perimeter of the new triangle will be 4.5 + 6 + 7.5 = 18 meters