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April 16th, 2012, 09:49 AM   #1
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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?
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April 16th, 2012, 11:12 AM   #2
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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?
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April 16th, 2012, 11:31 AM   #3
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Re: the biggest triangle

The area
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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.
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April 16th, 2012, 01:15 PM   #5
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Re: the biggest triangle

How can I prove it?
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December 30th, 2017, 12:15 AM   #6
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Can you prove that the three angles of a triangle sum to 180 degrees?
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December 30th, 2017, 07:48 AM   #7
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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.
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December 30th, 2017, 04:02 PM   #8
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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.
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December 30th, 2017, 06:04 PM   #9
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I suggest making a diagram.
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