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# What is the maximum area that can be enclosed by a triangle

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Director
Joined: 07 Jun 2004
Posts: 610

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Location: PA
What is the maximum area that can be enclosed by a triangle [#permalink]

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26 Jan 2005, 16:50
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What is the maximum area that can be enclosed by a triangle with perimeter = 12 cm

Kudos [?]: 924 [0], given: 22

CIO
Joined: 09 Mar 2003
Posts: 461

Kudos [?]: 71 [0], given: 0

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26 Jan 2005, 18:16
banerjeea_98 wrote:
Is the ans = 4(3^1/2) ?

I think it is. The biggest triangle here would be an equilateral one, each side length four. So the area is 4 root 3.

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VP
Joined: 18 Nov 2004
Posts: 1431

Kudos [?]: 45 [0], given: 0

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26 Jan 2005, 18:30
ian7777 wrote:
banerjeea_98 wrote:
Is the ans = 4(3^1/2) ?

I think it is. The biggest triangle here would be an equilateral one, each side length four. So the area is 4 root 3.

Although I was not sure of the equilateral or not initially, but we know that we need to maximize area of tri i.e. {s(s-a)(s-b)(s-c)}^1/2, where s = (a+b+c)/2 = 6......only way I saw that it can happen is when a=b=c=4

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Manager
Joined: 31 Aug 2004
Posts: 161

Kudos [?]: 15 [0], given: 0

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31 Jan 2005, 09:42
Can someone explain to me the formula "s(s-a)(s-b)(s-c)}^1/2" banerjeea_98 mentioned above?

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31 Jan 2005, 09:42
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