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655-705 (Hard)|   Geometry|      
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Bunuel
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What is the perimeter of an isosceles triangle PQR with integer sides 24 Nov 2021, 03:30
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55% (hard)

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54% (01:27) correct 46% (01:20) wrong based on 109 sessions

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What is the perimeter of an isosceles triangle PQR with integer sides if PQ = 6 cm?

(1) QR = 3 cm
(2) PR < 4 cm
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errorlogger
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What is the perimeter of an isosceles triangle PQR with integer sides 27 Nov 2021, 05:23
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Bunuel
What is the perimeter of an isosceles triangle PQR with integer sides if PQ = 6 cm?

(1) QR = 3 cm
(2) PR < 4 cm
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If the given triangle is isosceles. 2 sides will be equal.

1)QR = 3
Case1: PQ = QR = 3, Perimeter = 3 + 3 + 6 = 12

Case2: PQ = PR = 6, Perimeter = 6 + 6 + 3 = 15
Insufficient!
2)PR < 4
Clearly Insufficient!
Combining (1) & (2):
QR = PR = 3, PQ = 6, Perimeter = 6 + 3 + 3 = 15
IMO C!
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What is the perimeter of an isosceles triangle PQR with integer sides 29 Nov 2021, 11:32
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Can someone tell the answer?
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What is the perimeter of an isosceles triangle PQR with integer sides 01 Dec 2021, 10:49
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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


shalin23
Can someone tell the answer?
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Shreyaskn
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What is the perimeter of an isosceles triangle PQR with integer sides 14 Mar 2022, 22:16
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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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What is the perimeter of an isosceles triangle PQR with integer sides 05 Dec 2024, 08:16
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