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What is the greatest possible area of a triangular region

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Re: What is the greatest possible area of a triangular region  [#permalink]

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New post 28 Nov 2014, 02:15
I found this statement as a rule in a flashcard: "If you are given 2 sides of a triangle or a parallelogram, you can maximize the area by placing those two sides perpendicular." I had some concerns in appreciating this statement and I find it related to this question. Was able to understand the statement better when I solved this question.

For those who are unable to appreciate this statement from the flash card, hope this below example helps! Let's say we know that the 2 sides of a triangle are 4 and 3. The question asks when will the area of the triangle with 2 of these vertices be the maximum. Consider these 3 scenarios:
Attachment:
Triangles.png
Triangles.png [ 3.87 KiB | Viewed 1042 times ]

What do we see from the figure above? The triangle with 2 sides as perpendicular bisectors will have the greatest areas. If you knew this rule, this question would have been a cake walk! :)

Hope this helps! :-D
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What is the greatest possible area of a triangular region with o  [#permalink]

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New post 26 Oct 2015, 03:34
The height of the given triangle within circumference of the circle will be either one or less than that. Since Radi is 1. Therefore, to maximise area height as well as base have to be as high as possible. Since its given one of the points is at the centre, base=1 & max height=1; Hence answer=1\2.

Hope this helps.
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Re: What is the greatest possible area of a triangular region  [#permalink]

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New post 17 Jan 2016, 03:27
If you are given two sides of a triangle or parallelogram, you can maximize the area by placing those two sides perpendicular to each other.

1*1/2=1/2
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Re: What is the greatest possible area of a triangular region  [#permalink]

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New post 29 May 2018, 02:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the greatest possible area of a triangular region &nbs [#permalink] 29 May 2018, 02:02

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