GMAT PREP question

Question

Please help me with the solution

rp9999 · Answer

7-p470709?t=64343&hilit=+greatest+possible+area+of+a+triangular+region+#p470709

jimmyjamesdonkey · Answer

I'm pretty sure the OA on this is A. I've seen several post on other boards saying it is B, but I believe it to be A. The largest triangle is a equilateral triangle. Meaning the sides are 1,1,1 in this case. So we have a Area of 1/2 * 1 * height. The height in this case is 1^2 + height^2 = 1^2. Height = sqrt3/2. So Area he sqrt3/4.

rp9999 · Answer

What about a triangle for which the angle at the center of the circle is 90 degrees and the other two angles are 45 degrees (isosceles right angle triangle - 90-45-45)

For such a triangle, height = base = radius of the circle = 1

So, Area = 1/2 * base * height = 1/2 * 1 * 1 = 1/2 or 0.5 ( which is greater that sqrt(3)/4 or 0.433)

walker · Answer

I think it is B

my logic: let sides of a triangle are a,b,c where a=b=1 and begin in center of a circle. Now, imagine that a and b is very close and area is near 0. Begin to move b, increasing angle between a and b from 0 to 180. The area is 1/2*a*h. h is a height of the triangle and changes from 0 (angle=0 or 180) to b (angle=90). So, the maximum height is equal b=1 and the maximum area is 1/2*1*1=1/2

jimmyjamesdonkey · Answer

Upon 2nd thought it is prob B, but I thought a equilateral triangle is the triangle with the biggest area possible?

jimmyjamesdonkey · Answer

I thought a equilateral triangle provided the biggest area possible in a triangle, or is it a isosceles?

chineseburned · Answer

My practical approach to this problem is:

Ok, we know it is an equilateral or isoceles triangle. We can compute the area of the equilateral easily, but can we compute it for the isoceles? Well, not so easily unless it is a right triangle. Knowing how much the GMAT loves right triangles, probably this is the case here as well. So, compute the area of the right isoceles triangle as well - even easier since the two legs are of length 1 each. So, we end up with two areas which are choices A and B. Which one is the greater? The second one - so this is the answer.

iamcartic · Answer

To support 1/2 as the ans I can provide you the logic:

Area of a trangle is abSinC x 1/2 now max SineC can take is 1 hence the value in this case can be 1/2. Sorry solution is out of scope for gmat

GMAT PREP question

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards