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What is the greatest possible area of a triangular region

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What is the greatest possible area of a triangular region [#permalink] New post 22 Jul 2007, 20:30
What is the greatest possible area of a triangular region with one vertex at the center of circle of radius 1 and the other two on the circle?

sqrt3/4, 1/2, pi/4, 1, sqrt2

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Re: Area of the triangular region [#permalink] New post 22 Jul 2007, 20:47
bewakoof wrote:
What is the greatest possible area of a triangular region with one vertex at the center of circle of radius 1 and the other two on the circle?

sqrt3/4, 1/2, pi/4, 1, sqrt2


Triangle with largest area is an equilateral triangle. Since, one vertex is at the centre and the other 2 on the circle, side of the triangle is 1.

Hence, area = sqrt(3/4). A.
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 [#permalink] New post 23 Jul 2007, 12:44
Should be '1/2'

The greatest area will be of right angle triangle, with base and height equal to radius.
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 [#permalink] New post 24 Jul 2007, 07:05
Its not 1/2..

and pls show some work..

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 [#permalink] New post 24 Jul 2007, 10:13
"Triangle with largest area is an equilateral triangle."

Is this a theorem or smth? It makes sense, but how do you know?
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 [#permalink] New post 24 Jul 2007, 10:24
Hayabusa wrote:
"Triangle with largest area is an equilateral triangle."

Is this a theorem or smth? It makes sense, but how do you know?


I remember reading it somewhere, but cannot recollect where. Of course, I may be wrong. :(
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 [#permalink] New post 24 Jul 2007, 21:38
I agree it is 1/2

sqrt(3)/4 is less than 1/2
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 [#permalink] New post 25 Jul 2007, 14:38
Is the answer root of 2? If it is, I'll explain.
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 [#permalink] New post 25 Jul 2007, 16:34
bewakoof wrote:
Its not 1/2..

and pls show some work..


It should be 1/2. I am 100% sure.
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 [#permalink] New post 25 Jul 2007, 17:09
sumande wrote:
Hayabusa wrote:
"Triangle with largest area is an equilateral triangle."

Is this a theorem or smth? It makes sense, but how do you know?


I remember reading it somewhere, but cannot recollect where. Of course, I may be wrong. :(


Just guessing on this (based on sketches) - possibly the largest triangle that can be inscribed in a circle is equilateral, but if one vertex is the center of the circle, rather than on the circumference, then I agree it has to be a right triangle. So the area would be 1/2.
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 [#permalink] New post 25 Jul 2007, 17:22
By using Heron's formula, you can maximize the area of a triangle.

I asked a math wiz about it and he came up with root of 2.

I think he used differentiation.

Not sure if we are likely to see that on the GMAT.

Then again, I can be wrong....:)
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 [#permalink] New post 25 Jul 2007, 21:01
I have to dig my error log for the correct answer but I promise I'll do it tommorow.. I chose 1/2 and i got it wrong so i knew 1/2 wasnt the answer

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 [#permalink] New post 25 Jul 2007, 21:05
Here you go. Largest area is an equilateral triangle as stated by Heron's formula.

http://jwilson.coe.uga.edu/emt725/Heron/Heron.html
http://en.wikipedia.org/wiki/Heron's_formula
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 [#permalink] New post 25 Jul 2007, 21:44
bewakoof wrote:
I have to dig my error log for the correct answer but I promise I'll do it tommorow.. I chose 1/2 and i got it wrong so i knew 1/2 wasnt the answer


but it should be 1/2. make sure you do not have incorrect answer.
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 [#permalink] New post 26 Jul 2007, 09:43
Himalayan wrote:
bewakoof wrote:
I have to dig my error log for the correct answer but I promise I'll do it tommorow.. I chose 1/2 and i got it wrong so i knew 1/2 wasnt the answer


but it should be 1/2. make sure you do not have incorrect answer.


Equilateral Triangle has the largest area for a given PERIMETER>>>


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 [#permalink] New post 27 Jul 2007, 10:49
The perimeter is not set so the theorem doesn't hold. Could someone please explain why the answer is sqrt2?
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 [#permalink] New post 29 Jul 2007, 00:00
Area = 1/2 * 1 * 1 * sin90 = 1/2
Value of sin is max at 90 (i.e. 1)...so max area should be 1/2.
  [#permalink] 29 Jul 2007, 00:00
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