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

Question

. 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

rao · Answer

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

alpha_plus_gamma · Answer

The problem states "height" of the a general triangle; unless it's a right triangle "side" of a triangle can't be its height.

arjtryarjtry · Answer

mohindru... pls explain

walker · Answer

This is an example in which II statement can be false.

maratikus · Answer

I agree with E

walker, that was exactly the triangle I pictured in my head.

arjtryarjtry · Answer

so whats the ans....? walker... pls...

nmohindru · Answer

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?

walker · Answer

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.

arjtryarjtry · Answer

good explanattion and good participation... :lol:

scthakur · Answer

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?

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

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