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

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Which of the following about triangle must be true? I. If a [#permalink] New post 31 Jul 2008, 20:06
. 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
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Re: triangles roman nos. [#permalink] New post 31 Jul 2008, 20:23
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
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Re: triangles roman nos. [#permalink] New post 31 Jul 2008, 23:00
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.
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Re: triangles roman nos. [#permalink] New post 01 Aug 2008, 02:33
mohindru... pls explain
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Re: triangles roman nos. [#permalink] New post 01 Aug 2008, 04:44
Expert's post
This is an example in which II statement can be false.
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Re: triangles roman nos. [#permalink] New post 01 Aug 2008, 05:38
I agree with E

walker, that was exactly the triangle I pictured in my head.
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Re: triangles roman nos. [#permalink] New post 01 Aug 2008, 07:52
so whats the ans....? walker... pls...
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Re: triangles roman nos. [#permalink] New post 01 Aug 2008, 10:01
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?
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Re: triangles roman nos. [#permalink] New post 01 Aug 2008, 10:15
Expert's post
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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Re: triangles roman nos. [#permalink] New post 04 Sep 2008, 23:38
good explanattion

and good participation... :lol:
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Re: triangles roman nos. [#permalink] New post 05 Sep 2008, 00:18
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, 00:18
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