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$$ABCD$$ is a rectangle having area 8051. Its side lengths are integers. Then minimum perimeter possible for such rectangle is
$$8051 = 8100 - 49 = 90^2 - 7^2 = 83 \times 97$$, and 83 and 97 are primes. The only integer side pairs are $$1 \times 8051$$ and $$83 \times 97$$, and the perimeter is least for the closer pair. Minimum perimeter $$= 2(83 + 97) = 360$$.
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