ANSWER
P₁ = 10 millimeters
Step-by-step explanation
If the figures are similar, then one is a dilation of the other. As we can see in the side lengths, the larger rectangle has a side length that is 6 times the side length of the smaller rectangle.
Since the perimeter is linear, the perimeter of the smaller figure is the perimeter of the larger figure divided by the scale factor, which is 6,
Hence, the perimeter of the smaller rectangle is 10 mm.