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# How many of the three heights of triangle ABC do not pass inside the

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Math Expert
Joined: 02 Sep 2009
Posts: 49931
How many of the three heights of triangle ABC do not pass inside the  [#permalink]

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30 Mar 2017, 08:18
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Difficulty:

45% (medium)

Question Stats:

50% (01:26) correct 50% (01:25) wrong based on 35 sessions

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How many of the three heights of triangle ABC do not pass inside the triangle?

(1) ΔABC is obtuse.

(2) The altitude of A from BC does not pass inside ΔABC.

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Re: How many of the three heights of triangle ABC do not pass inside the  [#permalink]

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30 Mar 2017, 08:30
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St1: ABC is obtuse --> Suppose B is the obtuse angle and BC is the base. Project BC to a point D such that D is vertically below A then AD will be the height and will lie outside the triangle. Thus, there is one height that does not pass inside the triangle.

St2: The altitude of A from BC does not pass inside ΔABC. --> Sufficient.

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Re: How many of the three heights of triangle ABC do not pass inside the  [#permalink]

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03 Apr 2017, 09:13
I did not understand this question. Diagrams please?
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Joined: 29 Apr 2015
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Re: How many of the three heights of triangle ABC do not pass inside the  [#permalink]

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03 Apr 2017, 10:11
It seems like there may be some language translation issues in this problem. What are heights and altitudes in the context of triangles? Are these supposed to be lengths and angles?
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Re: How many of the three heights of triangle ABC do not pass inside the  [#permalink]

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03 Apr 2017, 10:14
ar500 wrote:
It seems like there may be some language translation issues in this problem. What are heights and altitudes in the context of triangles? Are these supposed to be lengths and angles?

Height and altitude are the same thing - the altitude of a triangle is the perpendicular from the base to the opposite vertex.

Check more here: https://gmatclub.com/forum/math-triangles-87197.html
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How many of the three heights of triangle ABC do not pass inside the  [#permalink]

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03 Apr 2017, 23:32
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SOUMYAJIT_ wrote:
I did not understand this question. Diagrams please?

Attached figure for your reference. Notice that height AD lies outside the obtuse angled triangle ABC.
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Triangle.png [ 4.18 KiB | Viewed 502 times ]

How many of the three heights of triangle ABC do not pass inside the &nbs [#permalink] 03 Apr 2017, 23:32
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