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# Which of the following about triangle must be true? I. If a

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Current Student
Joined: 11 May 2008
Posts: 552
Which of the following about triangle must be true? I. If a [#permalink]

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31 Jul 2008, 21:06
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

. Which of the following about triangle must be true?
I. If a triangle have sides a and b, the perimeter of the triangle must less than 2(a+b)
II. If two of the heights of a triangle are less than x, the perimeter of the triangle is less than 3x.
III. If one of the heights of the triangle is greater than x, the perimeter of the triangle is greater than 2x.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Director
Joined: 20 Sep 2006
Posts: 640

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31 Jul 2008, 21:23
arjtryarjtry wrote:
. Which of the following about triangle must be true?
I. If a triangle have sides a and b, the perimeter of the triangle must less than 2(a+b)
II. If two of the heights of a triangle are less than x, the perimeter of the triangle is less than 3x.
III. If one of the heights of the triangle is greater than x, the perimeter of the triangle is greater than 2x.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

IMO E;

I
one side : a
second side: b
third side must be less than a+b ==> hence perimeter must be less than a+b+(a+b)

II

If two sides are more than x; third side must be more than the diff of other two sides. INSUFF

III
one side : x
other two sides sum must be greater than x (worst case scenario summ of other two sides = x i.e all the 3 co-ordinates are on one line)

perimeter = x + more than x = more than 2x
Director
Joined: 14 Aug 2007
Posts: 704

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01 Aug 2008, 00:00
rao_1857 wrote:
arjtryarjtry wrote:
. Which of the following about triangle must be true?
I. If a triangle have sides a and b, the perimeter of the triangle must less than 2(a+b)
II. If two of the heights of a triangle are less than x, the perimeter of the triangle is less than 3x.
III. If one of the heights of the triangle is greater than x, the perimeter of the triangle is greater than 2x.

II

If two sides are more than x; third side must be more than the diff of other two sides. INSUFF

III
one side : x
other two sides sum must be greater than x (worst case scenario summ of other two sides = x i.e all the 3 co-ordinates are on one line)

perimeter = x + more than x = more than 2x

The problem states "height" of the a general triangle; unless it's a right triangle "side" of a triangle can't be its height.
Current Student
Joined: 11 May 2008
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01 Aug 2008, 03:33
mohindru... pls explain
CEO
Joined: 17 Nov 2007
Posts: 3525
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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01 Aug 2008, 05:44
This is an example in which II statement can be false.
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Director
Joined: 01 Jan 2008
Posts: 605

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01 Aug 2008, 06:38
I agree with E

walker, that was exactly the triangle I pictured in my head.
Current Student
Joined: 11 May 2008
Posts: 552

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01 Aug 2008, 08:52
so whats the ans....? walker... pls...
Senior Manager
Joined: 06 Apr 2008
Posts: 401

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01 Aug 2008, 11:01
walker wrote:
I vote for E

Well what if you have a triangle with one angle of 1 degree and x is height from this angle to base of other side , do you still think perimeter will be gr8 then 2x?
CEO
Joined: 17 Nov 2007
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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01 Aug 2008, 11:15
a height is always less or equal adjacent sides. Therefore, the sum of adjacent sides is greater than 2x, so is the perimeter. If you think it is incorrect, try to draw the triangle that refutes this rule.
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Current Student
Joined: 11 May 2008
Posts: 552

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05 Sep 2008, 00:38
good explanattion

and good participation...
SVP
Joined: 17 Jun 2008
Posts: 1504

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05 Sep 2008, 01:18
II mentions that two of heights are less than x.....what two heights are being referenced here? If I assume that two heights are two sides, the perimeter will definitely be less than 3x.......am I reading something wrong here?
Re: triangles roman nos.   [#permalink] 05 Sep 2008, 01:18
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# Which of the following about triangle must be true? I. If a

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