Ellipses Inscribed in an Isosceles Triangle

Geometry Level pending

An isosceles triangle has a base of 20 and a height of 30. An ellipse having the ratio of the major axis to minor axis lengths equal to 2, is to be inscribed in the triangle, with the condition that its axes are parallel to the coordinate axes, that is, horizontal and vertical. It turns out that there are two possible ellipses, as shown in the figure above. Find the sum of their major axes.

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