GMAT Math : DSQ: Calculating the perimeter of an equilateral triangle
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Example Question #101 : Triangles
Which, if either, of equilateral triangles 
Statement 1:
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.
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.
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.
If we let 
Statement 1:
Statement 2:
Since the perimeter of an equilateral triangle is three times its common sidelength, comparison of the lengths of the sides is all that is necessary to determine which triangle, has the greater perimeter. The question can therefore be reduced to asking which of 
Statement 1 alone is not sufficient to yield an answer:
Case 1:
Case 2:
Both cases satisfy Statement 1, but in the first case, 
Now assume both statements to be true. The two equations together comprise a system of equations:
Multiply the first equation by 3 and the second by 
Now substitute back:
Example Question #102 : Triangles
Given an equilateral triangle 
Statement 1:
Statement 2:
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient 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.
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.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Assume Statement 1 alone. Since in 
and 
Statement 2 alone gives insufficient information, since we know nothing about the second leg or the hypotenuse of
Case 1: Let 
Case 2: Let 
Example Question #103 : Triangles
Find the perimeter of the equilateral triangle.
- A side measures
.
- The area is
.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Each statement alone is sufficient to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Each statement alone is sufficient to answer the question.
Recall the formula for perimeter of a triangle.
where 
Statement 1: We're given the length of the side so all we need to do is plug this value into the equation.
Statement 2: We're given the area so we first need to solve for the side length.
Now we can plug the value into the equation, like we did in Statement 1.
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