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marcodonzelli
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Are all angles of triangle ABC smaller than 90 degrees? 1. 02 Mar 2008, 08:55
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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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Are all angles of triangle ABC smaller than 90 degrees? 1. 02 Mar 2008, 11:48
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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.
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Are all angles of triangle ABC smaller than 90 degrees? 1. 02 Mar 2008, 12:41
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sreehari
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.
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it's not just A? can't B represent the long and the middle side being longer than the shortest?
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Are all angles of triangle ABC smaller than 90 degrees? 1. 02 Mar 2008, 14:05
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dominion
sreehari
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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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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Are all angles of triangle ABC smaller than 90 degrees? 1. 02 Mar 2008, 22:41
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sreehari
dominion
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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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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



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!