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April 16th, 2012, 10:49 AM  #1 
Senior Member Joined: Nov 2011 Posts: 248 Thanks: 3  the biggest triangle
What is the biggest triangle that can be draw in a sides's rectangle of x and y? How can I denote it by x and y? Is there an expression to its side by using x and y? 
April 16th, 2012, 12:12 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: the biggest triangle
What do you mean by biggest triangle? The largest area or perimeter? Do we know how x and y are related?

April 16th, 2012, 12:31 PM  #3 
Senior Member Joined: Nov 2011 Posts: 248 Thanks: 3  Re: the biggest triangle
The area

April 16th, 2012, 12:44 PM  #4  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond  Re: the biggest triangle Quote:
 
April 16th, 2012, 02:15 PM  #5 
Senior Member Joined: Nov 2011 Posts: 248 Thanks: 3  Re: the biggest triangle
How can I prove it?

December 30th, 2017, 01:15 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond 
Can you prove that the three angles of a triangle sum to 180 degrees?

December 30th, 2017, 08:48 AM  #7 
Senior Member Joined: Sep 2016 From: USA Posts: 556 Thanks: 321 Math Focus: Dynamical systems, analytic function theory, numerics 
I would prove it as follows: 1. Argue that the corners of the largest triangle must lie on the perimeter of the rectangle. 2. Argue that the largest triangle whose corners lie on the perimeter must have its corners coincide with 3 of the 4 rectangle corners. 
December 30th, 2017, 05:02 PM  #8 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 632 Thanks: 85 
Obviously if you can increase the height and keep the base the same or increase the base and keep the height the same, the area will get larger. If any points of the triangle were not a corner of the rectangle, you could increase the height or base without decreasing the other one.

December 30th, 2017, 07:04 PM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond 
I suggest making a diagram.


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