Finding the maximum area of a rectangle with an inscribed triangle

Kabir Sheth shared this problem 3 weeks ago

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I would like to determine a formula that describes the maximum possible area of a rectangle that has an inscribed non-right 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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Comments (9)

Michael Borcherds ● 2 weeks ago

Is this helpful? (by mathmagic)

https://www.geogebra.org/

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Kabir Sheth ● 2 weeks ago

Yes it is. Thank you!

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mathmagic ● 2 weeks ago

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

Files: foro.ggb

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Kabir Sheth ● 2 weeks ago

Thanks for the help! I will definitely use this.

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mathmagic ● 2 weeks ago

I think file at bottom is better

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rami ● 2 weeks ago

@Kabir Sheth

I think mathmagic mean his own file at bottom (not my file "formula01.ggb")

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rami ● 2 weeks ago

If I understand the question correct then the maximum of triangle-area 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...)

Files: formula01.ggb

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Kabir Sheth ● 2 weeks ago

Thank you!

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mathmagic ● 2 weeks ago

I think the G is higher when D is in the middle of p in attached

Files: foro.ggb

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