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You can pick any side to be the base. It doesn't really matter.
It can be any length at all. The length of one side imposes no limits at all on the altitude.
any side of the triangle that is perpendicular to the height.
Yes, though generally speaking the bottom, horizontal side (if any) of a triangle is called its base.
The orthocenter of a triangle may lie outside the triangle since the ___altitude___ may not intersect any side of the triangle. * * * * * No. One of the altitudes must intersect the side opposite it and so it is not correct to say ANY side of the triangle.