Build a Triangle IV

Given: A line segment (purple) whose length is fixed and known. Given also a line segment (blue) of fixed length drawn to its midpoint and a third line segment (green) of fixed length perpendicular to it. Is it {always, sometimes, never} possible to build a triangle which has one of the line segments as a side and the line segments are a median and an altitude to that side? What questions could / would you put to your student based on this applet?
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