Data Sufficiency

sampath wrote:Is the perimeter of a triangle greater than 1?
(1) Two of the heights are less than 1/3
(2) One of the heights is greater than 1/2

Statement 1: This doesn't give us any idea about the length of the sides of the triangle.

Not sufficient

Statement 2: Refer to the following figure,

Triangle AMC and BMC are right angled triangle with AC and BC as hypotenuses respectively. Hence, both AC and BC are greater than CM. If the height CM is greater than 1/2 then the sides AC and BC must be greater than 1/2 too. Thus the perimeter of the triangle must be greater than 1.

Sufficient

The correct answer is B.