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If ∆ABC is an isosceles triangle, what is the

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If ∆ABC is an isosceles triangle, what is the  [#permalink]

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New post 19 Sep 2018, 06:44
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If ∆ABC is an isosceles triangle, what is the perimeter of ∆ABC?

(1) AB = 10√3
(2) AC = 8

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Re: If ∆ABC is an isosceles triangle, what is the  [#permalink]

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New post 19 Sep 2018, 07:05
1
(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
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Re: If ∆ABC is an isosceles triangle, what is the  [#permalink]

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New post 20 Sep 2018, 13:31
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GMATPrepNow wrote:
If ∆ABC is an isosceles triangle, what is the perimeter of ∆ABC?

(1) AB = 10√3
(2) AC = 8


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

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Re: If ∆ABC is an isosceles triangle, what is the &nbs [#permalink] 20 Sep 2018, 13:31
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