What is the perimeter of an isosceles triangle PQR with integer sides

Statement 1 is not sufficient because of the triangle inequality theorem which states: the sum of any 2 sides of a triangle must always be greater than the 3rd side.

We know one side is 6.

S1: we are given the other side as 3

There are 2 possibilities for an isosceles triangle, in which 2 of the side lengths are equal:

Case 1: 3 - 3 - 6

However, this does not form a valid triangle

3 + 3 = 6

Therefore, it must be that the 3rd unknown side is equal to = 6

Case 2: 6 - 6 - 3

Perimeter = 15 - unique value so S1 is Sufficient alone.

S2: we are told that the other side PR < 4

And we are given that the side must be integers

If we allow the 2 equal sides to be 6 and 6, then PR would be the non equal side.

PR in this scenario can take the following integer values: 1, 2, or 3

6 - 6 - 3

3 + 6 > 6 ——-> valid triangle


6 - 6 - 2

2 + 6 > 6 ———> valid triangle


As this two cases provides us with valid isosceles triangles within the constraints of statement 2 and the question stem, we can stop here.

The perimeter can vary and we do not get a unique answer. S2 is not sufficient


A - s1 alone is sufficient



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Statement 1 is correct because, if QR is three then other unknown side must be less than 9 and greater than 3. Therefore PR will be 6 as triangle is isosceles..

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