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 April 16th, 2012, 09:49 AM #1 Senior Member   Joined: Nov 2011 Posts: 250 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, 11:12 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 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, 11:31 AM #3 Senior Member   Joined: Nov 2011 Posts: 250 Thanks: 3 Re: the biggest triangle The area
April 16th, 2012, 11:44 AM   #4
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Re: the biggest triangle

Quote:
 Originally Posted by shaharhada 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?
xy/2.

 April 16th, 2012, 01:15 PM #5 Senior Member   Joined: Nov 2011 Posts: 250 Thanks: 3 Re: the biggest triangle How can I prove it?
 December 30th, 2017, 12:15 AM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond Can you prove that the three angles of a triangle sum to 180 degrees?
 December 30th, 2017, 07:48 AM #7 Senior Member   Joined: Sep 2016 From: USA Posts: 609 Thanks: 378 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, 04:02 PM #8 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 639 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, 06:04 PM #9 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond I suggest making a diagram.

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