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As all dimensions are integers, we just need to find out the smallest square that is bigger than 1845 and is divisible by 4 to find out the smallest perimeter. (Imaging the four corner squares are filled, the figure will be a big square.)

43²=1849

1849-1845 = 4 (divisible by 4)

So the smallest perimeter is 4 x 43 =172 cm

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