So you've been modeling a character/asset and you need to extrude a perfect square but what you have at the place you need to extrude from is a rectangle with no idea what the length and width is and the width isn't likely to be half the length for an edge loop in the centre to work. How can you make it into a square? doesn't seem to be an easy way to do this from what I can find.
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But Noth's method does work, though it takes a bit more effort than is ideal, if you'll be doing it a lot.