we can infer that the properties of heights will be same as that of the sides.
now from point 1
two of the sides are less than 2
in that case their sum can either be greater than or less than 3 so the third side will also can be greater or less than 3
hence this condition is in sufficient

From cond 2..one of the side is greater than 3 hence sum of other two side is greater than 3 so the perimeter is greater than 3--sufficient
hence ans is B

liferocks wrote:we can infer that the properties of heights will be same as that of the sides.

what :O ?

Sad to see so few response to what is a very good Question
@ liferocks I have the same answer but differ a wee bit

Is the perimeter of a triangle greater than 6?
1) Two of the heights are less than 2
2) One of the heights is greater than 3

from 2) height > 3 i.e. the percendicular from the vertex to the base is > 3
which is the shortest distance from the vertex to the base.
therefore the two adjacent sides from the vertex to the base has to be each > 3
so the perimeter is > 6

1) if heights are less than 2 they can be even < 1 or
the heights of an equilateral triangle of side 2 will satisfy the condition cos the heights are 3¹/² = 1.4~
but the perimeter is 6
IMO B