Finding the maximum area of a rectangle with an inscribed triangle

Kabir Sheth shared this problem 3 months ago
Solved

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.

Comments (9)

photo
1

Is this helpful? (by mathmagic)

https://www.geogebra.org/

photo
1

Yes it is. Thank you!

photo
photo
1

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
photo
1

Thanks for the help! I will definitely use this.

photo
1

I think file at bottom is better

photo
1

@Kabir Sheth

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

photo
photo
1

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...)

photo
1

Thank you!

photo
photo
1

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

Files: foro.ggb
© 2019 International GeoGebra Institute