. 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
one side : a
second side: b
third side must be less than a+b ==> hence perimeter must be less than a+b+(a+b)
If two sides are more than x; third side must be more than the diff of other two sides. INSUFF
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