GMAT Math : DSQ: Calculating the perimeter of an acute / obtuse triangle
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Example Question #11 : Dsq: Calculating The Perimeter Of An Acute / Obtuse Triangle
What is the perimeter of 
Statement 1: The triangle with its vertices at the midpoints of 
Statement 2: 
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Assume Statement 1 alone. A segment that has as its endpoints the midpoints of two sides of a triangle is a midsegment of the triangle, and its length is half that of the side to which it is parallel. Therefore, the sum of the lengths of the midsegments—that is, the perimeter of the triangle they form, which from Statement 1 is 34, is half the perimeter of the larger triangle, which here is 
Assume Statement 2 alone. Here, 
Example Question #12 : Dsq: Calculating The Perimeter Of An Acute / Obtuse Triangle
True or false: The perimeter of 
Statement 1: 
Statement 2: 
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Assume both statements to be true. An isosceles triangle has two sides of equal length, so either 
and
If 
If 
Without further information, it is impossible to determine whether the perimeter is less than or greater than 60.
Example Question #13 : Dsq: Calculating The Perimeter Of An Acute / Obtuse Triangle
What is the perimeter of
Statement 1: 
Statement 2:
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
From Statement 1 alone, we know that two sides are of length 10, but we are not given any clue as to the length of the third. Therefore, we cannot calculate the sum of the side lengths, which is the perimeter. Statement 2 alone is unhelpful, since it only gives that two angles have equal measure; applying the Converse of the Isosceles Triangle Theorem, it can be determined that their opposite sides 
Now assume both statements to be true. From Statement 1, 
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