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Обсуждение задачи 1874. Футбольные ворота

What shape is the football gate?
Послано Nodir NAZAROV Komiljonovich 30 янв 2014 20:17
I tried to figure it out, how 1 tree and two sticks with the length of 2 can form the area more than 4? The largest area would be rectangle. What is the trick on this problem, can anybody explain with Geometry language.

Thanks.
Re: What shape is the football gate?
Послано Andrew Sboev [USU] 30 янв 2014 21:48
The key point of the problem statement is
"She knew that the standard football goal was rectangular, but, being creative, she assumed that her goal could have the form of an arbitrary quadrangle."
So, it may be not a rectangle.
Re: What shape is the football gate?
Послано Nodir NAZAROV Komiljonovich 6 фев 2014 22:44
I tried trapezoid like:

   /|
 2/_|
 |  |
2|__|
   x

and tried to maximize the function - f(x) for total area which answer is sqrt(3) and total area is ~4.33
How to get ~4.8 for the given test?