The perimeter of which of the above triangles can be determined from

III definitely doesn't work. D and E are out.
II definitely does work. A is out.

Let's look at I. Draw a horizontal line on a piece of paper length 5. I don't care if it's centimeters, inches, or miles (if you have a really big piece of paper). Now, use a protractor (or just your imagination) to draw a line up and to the right from the left-most point of the first line, and be sure that the angle between the first line and the second is 65 degrees. There's only one way you can draw the second line; it has to go EXACTLY where it is. Now, use a protractor (or just your imagination) to draw a line up and to the left from the right-most point of the first line, and be sure that the angle between the first line and the third is 55 degrees. There's only one way you can draw the third line; it has to go EXACTLY where it is. That means there is only one way to draw a triangle with side 5 that is adjacent on one end to an angle of 65 degrees and adjacent on the other end to an angle of 55 degrees. If there's only one way to draw the triangle, there has to be a way to find the other sides. So, I works. B is out.

Answer choice C.


I think this part is beyond the scope of what the GMAT tests, but I'll cover it for those of who just LOVE to get caught up in material that isn't on the test in order to satisfy your intellectual curiosity (I feel your pain!)

Using the Rule of Sines, we can find \(A=5\frac{sin(60)}{sin(55)}\) and \(B=5\frac{sin(60)}{sin(65)}\), so A=4.729 and B=5.233. That means the perimeter is 5+4.729+5.233 = 14.962.