If ∆ABC is an isosceles triangle, what is the

Question

If ∆ABC is an isosceles triangle, what is the perimeter of ∆ABC?

(1) AB = 10√3
(2) AC = 8

GMATBusters · Answer

(1) AB = 10√3 = 17.3
other sides are unknown ,  NOT SUFFICIENT  to find perimeter.

(2) AC = 8, other sides are unknown ,  NOT SUFFICIENT  to find perimeter.

Combining Statement 1 & 2, AB= 1,7.3, AC = 8
As the  triangle ABC is an isosceles ,triangle, hence BC can be 8 or 17.3

but if AB = 8, sides of triangle are 8,8,17.3 which is impossible as
 " in a triangle sum of two sides must be greater than third side" 
but here  8+8<17.3.  hence AB can not be equal to 8.
 Hence, AB = 17.3 , here 8+17.3>17.3
Three sides are 8, 17.3, 17.3. hence perimeter can be determined, 
 Answer = C

BrentGMATPrepNow · Answer

Target question :    What is the perimeter of ∆ABC?

Given : ∆ABC is an  isosceles  triangle

Statement 1 : AB = 10√3  
We only know the measurement of ONE side of the triangle. 
So, there's no way to determine the triangle's perimeter. 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : AC = 8  
We only know the measurement of ONE side of the triangle. 
So, there's no way to determine the triangle's perimeter. 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that AB = 10√3
Statement 2 tells us that AC = 8
We also know that ∆ABC is an isosceles triangle, so  two sides have the same length . 
This means there are two possible cases: the sides have length 10√3, 10√3 and 8 OR the sides have length 10√3, 8 and 8

Since we have two different sets of lengths, we might incorrectly conclude that the statements COMBINED are not sufficient. 
However, there's an important rule about the side lengths of a triangle:

If two sides of a triangle have lengths A and B, then . . . 
  DIFFERENCE between A and B < length of third side < SUM of A and B   
In other words, the length of ONE side of a triangle cannot be longer than the sum of the other TWO sides.

For the GMAT, all students should have the following approximations memorized: 
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
So, 10√3 ≈ (10)(1.7) ≈ 17

Let's rewrite our two possible cases: the sides have length 17, 17 and 8 OR the sides have length 17, 8 and 8 
Notice that, in the second case, the side with length 17 is longer than the sum of the other two sides (8 and 8)
This means the 17, 8, 8 triangle CANNOT EXIST
 
Since the first case (17, 17, 8) does not break any rules, we can be certain that ∆ABC has lengths 10√3, 10√3 and 8, which means we can definitely determine the perimeter. 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=sf5GkSd_1nQ

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If ∆ABC is an isosceles triangle, what is the

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GMAT Data Sufficiency (DS) Questions

If ∆ABC is an isosceles triangle, what is the

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