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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]  02 Mar 2008, 07:55
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: geo [#permalink]  02 Mar 2008, 10:48
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Based on pythagorean theorem - if square of longer side is less then sum of squares of other two sides, it's an acute traingle, and obtuse if it is graterthan, and right if they are equal.

1 - sufficient..assuming AB=x whic is the longer side x2 > (x/2)^2 + (2x/3)^2, so the triangle is obtuse.

2 - sufficient..it's an acute triangle, so all angles are lessthan 90.
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Re: geo [#permalink]  02 Mar 2008, 11:41
sreehari wrote:
D

Based on pythagorean theorem - if square of longer side is less then sum of squares of other two sides, it's an acute traingle, and obtuse if it is graterthan, and right if they are equal.

1 - sufficient..assuming AB=x whic is the longer side x2 > (x/2)^2 + (2x/3)^2, so the triangle is obtuse.

2 - sufficient..it's an acute triangle, so all angles are lessthan 90.

it's not just A? can't B represent the long and the middle side being longer than the shortest?
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Re: geo [#permalink]  02 Mar 2008, 13:05
dominion wrote:
sreehari wrote:
D

Based on pythagorean theorem - if square of longer side is less then sum of squares of other two sides, it's an acute traingle, and obtuse if it is graterthan, and right if they are equal.

1 - sufficient..assuming AB=x whic is the longer side x2 > (x/2)^2 + (2x/3)^2, so the triangle is obtuse.

2 - sufficient..it's an acute triangle, so all angles are lessthan 90.

it's not just A? can't B represent the long and the middle side being longer than the shortest?

No, whatever sides you chose it's got to be acute which means all angles are lessthan 90. Keep in mind that we are talking about squares here. By definition of triangle longest side must be less than the sum of other two sides, but it doesn't tell you the triangle type.
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Re: geo [#permalink]  02 Mar 2008, 21:41
sreehari wrote:
dominion wrote:
sreehari wrote:
D

Based on pythagorean theorem - if square of longer side is less then sum of squares of other two sides, it's an acute traingle, and obtuse if it is graterthan, and right if they are equal.

1 - sufficient..assuming AB=x whic is the longer side x2 > (x/2)^2 + (2x/3)^2, so the triangle is obtuse.

2 - sufficient..it's an acute triangle, so all angles are lessthan 90.

it's not just A? can't B represent the long and the middle side being longer than the shortest?

No, whatever sides you chose it's got to be acute which means all angles are lessthan 90. Keep in mind that we are talking about squares here. By definition of triangle longest side must be less than the sum of other two sides, but it doesn't tell you the triangle type.

OA is A.
1. gives the relationship b/w sides and thus the shape of the triangle.
2. it says that the triangle could be acute as well as right. hp^2 + side1^2>side2^2
Re: geo   [#permalink] 02 Mar 2008, 21:41
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