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Is triangle ABC isosceles? [#permalink]
09 Dec 2010, 06:52

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anilnandyala wrote:

is the triangle iscoceles

1 x not equal to y 2 ab/bc = 2

Attachment:

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Is triangle ABC isosceles?

(1) X does not equal Y --> angles at the side BC are not equal --> \(AB\neq{AC}\), but the third side, BC, can be equal to either of them. Not sufficient.

(2) AB/BC=2 --> AB=2BC --> \(AB\neq{BC}\), but AB can be equal to AC. Not sufficient.

(1)+(2) As \(AB\neq{AC}\) and \(AB\neq{BC}\) then the only way triangle ABC to be an isosceles is AC to be equal to BC, but in this case AB=2BC=2AC=BC+AC --> but the length of any side of a triangle must be smaller than the sum of the other two sides, so AB must be less than BC+AC, hence the case when AC=BC is not possible: triangle ABC is not isosceles. Sufficient.

Re: Is triangle ABC isosceles? [#permalink]
10 Dec 2013, 13:17

Is triangle ABC isosceles?

(1) X does not equal Y --> angles at the side BC are not equal --> , but the third side, BC, can be equal to either of them. Not sufficient.

Tells us nothing. X ≠ Y but the third angle could equal x or y in which case the triangle would be isosceles or the third angle would = w in which case the triangle would not be isosceles. Insufficient.

(2) AB/BC=2

The length of AB is twice the length of BC but we don't know anything about side AC. Insufficient.

1+2) The only way for this triangle to be isosceles is if a.) AC = BC or b.) AB = AC. Neither of these outcomes are possible. If AC = AB then a triangle wouldn't be possible. In any triangle, the sum of two legs must be greater than the third. If AC = BC then the formula for the triangle would be 2BC = BC + BC which isn't possible. We also know that AC ≠ AB because the angles opposite them, x and y respectively, do not equal one another. Thus, AC cannot = AB and AC is a different length than AB. This triangle CANNOT be isosceles. SUFFICIENT.

C

gmatclubot

Re: Is triangle ABC isosceles?
[#permalink]
10 Dec 2013, 13:17

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