Let S be the length of the short side of the fence.
Thus, the length of a long side of the fence is 3S.
There are 2 of each side, so the whole fence is 2S + 2 * 3S = 2S + 6S = 8S long.
The whole fence is 8S = 640 feet long.
Thus, the short side of the fence that needs to be replaced is S = 640 / 8 = <<640/8=80>>80 feet long.
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