CAT 1 - trouble with triangles

[jeremy.hansen]

Question name Is It Isosceles

having trouble with a DS question in which I have to determine whether a triangle ABC is isosceles. I am fine up until the point where I look at 1 & 2 combined.

1) angle ABC (X) does not equal ACB (Y)
2) AB/BC = 2

I get to this part which is based on the statement 2 AB/BC = 2.

Since BC is half the length of AB, AC must then also be half the length of AB. But then AC + BC = AB, which violates the triangle inequality (ABC would not be a triangle; these three sides would form back-to-back line segments if placed together in an attempt to form a triangle). Thus the triangle cannot be isosceles.

I understand the part that AC + BC must equal AB for it to be an isosceles triangle but do not understand why this cannot be possible. If for example AB = 8 & BC = 4 then I thought the range of AC could be between 4 (8-4) & 12 (8+4).

I assume this goes back to statement 1 but I am unsure as to how to apply.



ty

[mschwrtz]

The short answer is the 4<AC<8, NOT 4<AC<8.

Imagine three line segments of length 4, 4, and 8. If you tried to join them to form a triangle, you'd get a straight line.

If I tell you that A, B, and C all lie on a plane, and you don't mind if they all lie in a straight line, then you can infer that AB-BC<AC<AB+BC. If I tell you that A, B, and C form a triangle, then you can infer that AB-BC<AC<AB+BC.

[hiral.j567]

hi mschwrtz,

From St (2), we have the ratio of two sides AB/BC = 2:1, since an isosceles triangle cannot have any of its sides in the ratio 2:1...
and the sides necessarily have to be in the ratio 1:1:sqrt(2) ,
doesnt (2) suffice to say that the triangle is not an isosceles triangle ?

[hiral.j567]

Got my GMAT in a couple of days ... any help guys??

[mschwrtz]

1) A triangle with sides of length 2, 2, and 1 would be isosceles, though not right isosceles.

2) Sorry that we didn't get back to you before your exam.

3) When you bump a thread, it just takes that much longer to get a response. We answer the oldest questions first.