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# Are all angles of triangle ABC smaller than 90 degrees? 1.

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Are all angles of triangle ABC smaller than 90 degrees? 1. [#permalink]  26 May 2008, 02:43
Are all angles of triangle ABC smaller than 90 degrees?

1. 2AB=3BC=4AC
2. AC^2 + AB^2 > BC^2
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Re: M17-4 [#permalink]  26 May 2008, 12:17
sondenso wrote:
Are all angles of triangle ABC smaller than 90 degrees?

1. 2AB=3BC=4AC
2. AC^2 + AB^2 > BC^2

A

you have AB = 2, AC = 1, so for it to be a 30-60-90 triangle, BC has to be = sqrt(3) = ~1.7

But from the statement, BC is only 2/3 of AB, so it is not a 30-60-90 triangle, and BC is only ~1.3, so one of the angle has to be bigger than 90

statement 2 does not tell you about the ratio or relationship between the 3 sides. You can have a equilateral, or types of isoceles triangles.
Re: M17-4   [#permalink] 26 May 2008, 12:17
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