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Finding the maximum area of a rectangle with an inscribed triangle
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I would like to determine a formula that describes the maximum possible area of a rectangle that has an inscribed nonright triangle which shares a vertex with the rectangle. Attached is my work so far. Is there a software I can use to test this formula or can anyone confirm that it is correct? Thanks.
Files:
MathIA Work.docx
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Is this helpful? (by mathmagic)
https://www.geogebra.org/
for testing is simple
open the attached, select D (red point) and press the arrows until rectangle is maximum
then create the angle or segment you predict and compare
more elaborate files can do it automatically
If I understand the question correct then the maximum of trianglearea is very, very, ....... very near the half area of rectangle (max triangle = Distance(B,C) Distance(A,B) /2  1/∞)
In the attachment the points E and F are never equal a rectangle corner AND all angles of triangle are never 90° (but both conditions: can be very near...)
I think the G is higher when D is in the middle of p in attached
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