Question: Perimeter = Sum of three sides = ?

Statement 1: AB = 5

NOT SUFFICIENT

Statement 2: AC = 12

NOT SUFFICIENT

COmbining the statements

BC is still unknown hence

NOT SUFFICIENT

Answer: Option E
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VERITAS PREP OFFICIAL SOLUTION:

And it’s common (in fact a similar problem shows that about 55% of people make this exact mistake) to think “oh well this is a 5-12-13, so both statements together prove that side BC is 13 and I can calculate that the perimeter is 30 meters.” But wait – 5 and 12 only lead to a third side of 13 when you know that 5 and 12 are the short sides. If you don’t know that, the triangle could fit the Pythagorean Theorem with 12 as the hypotenuse, meaning that you’re solving for side b:

5^2 + b^2 = 12^2, so 25 + b^2 = 144, and b then equals the square root of 119.

So while it’s critical that you memorize these four right triangle ratios, it’s just as important that you don’t fall so in love with them that you use them even when they don’t apply.
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Trying to think of this spatially, but different triangles can be produced given the dimensions of two sides depending upon the angle BAC? Of Course the size of the third side would be restricted between 7 and 19, but the exact dimension would be dictated by the angle BAC?

I voted C, thinking that only 1 unique triangle can be prepared given the above dimensions.