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What is the greatest possible area of a triangular region

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RonPurewal
 Post subject: Re: What is the greatest possible area of a triangular region
 Post Posted: Mon Sep 12, 2011 4:32 am 
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ManhattanGMAT Staff


Posts: 7146
me.parashar wrote:
thanks christiancryan. I too, answered the question wrong (marked obvious A). And the way you explained the question, I now know a very important concept of working the maxima-minima without the differential, and the beauty is that the concept can be used everywhere from number system to coordinate geometry.


good.

also, don't forget that the only mathematics required for this exam is the stuff up to and including high-school algebra and geometry. therefore, if you find yourself employing calculus, trigonometry, etc. in an attempt to solve one of these problems, you can rest assured that you are overcomplicating the issue.
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sergiolopez
 Post subject: Re: What is the greatest possible area of a triangular region
 Post Posted: Sun Oct 23, 2011 8:44 pm 
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Prospective Students


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I tried in this way:

First I calculated the maximum square that could fit in a triangle. I know that the diagonal=2 then the side S=2/SQRT(2) and as a consequence the area is S^2=2. The triangle is 1/4 of the area of the square --> A=1/2

Answer is B
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Abhilash Paul
 Post subject: Re: What is the greatest possible area of a triangular region
 Post Posted: Fri Oct 28, 2011 9:31 am 
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Students


Posts: 1
I did it this way. Area of a triangle can also be = 1/2 * ab * cos(x)
where a, b are two sides of the triangle, and x is the included angle.
Max area is when cox(x) is max (cos(x) is max for x= 90 deg and = 1)
So the answer is 1/2 *ab = 1/2 if you take the two sides as the radius of the circle, =1 in this case.
This explanation may prob be out of the scope of GMAT, not sure but this sure was a very fast method.
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RonPurewal
 Post subject: Re: What is the greatest possible area of a triangular region
 Post Posted: Wed Nov 09, 2011 6:53 am 
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ManhattanGMAT Staff


Posts: 7146
Abhilash Paul wrote:
I did it this way. Area of a triangle can also be = 1/2 * ab * cos(x)
where a, b are two sides of the triangle, and x is the included angle.
Max area is when cox(x) is max (cos(x) is max for x= 90 deg and = 1)
So the answer is 1/2 *ab = 1/2 if you take the two sides as the radius of the circle, =1 in this case.
This explanation may prob be out of the scope of GMAT, not sure but this sure was a very fast method.


no trigonometry is required on the gmat, but, on one out of several hundred problems, it may help.
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