Is the perimeter of a triangle greater than 1?

Question

(1) Two of the heights are less than 1/3 
(2) One of the heights is greater than 1/2

Professor · Answer

B.   a side with 1/2 length makes the sum of other two sides at least > than 1/2, making P greater than 1  .

ps_dahiya · Answer

I agree that answer is B but if one side is greater than 1/2 then it does not mean that one more side will be greater than 1/2. Instead, sum of other two sides will be greater than 1/2 making perimeter greater than 1/2.

veenu08 · Answer

can someone please explain the logic for this question

blueseas · Answer

STATEMENT 1 : 
Two heights are less than 1/3
see in figure:==> 2 triangles are there ABC and DEF
Perpendiclar from B to AC..and perpendicular from C to AB===>LESS THAN 1/3...But we can take point much higher shown....lets perpendicular from A to BC..is 100 ..SO IN THIS case perimeter you can see will be  more than 1 .
take second triangle DEF ===>IN this all the heights are very smalll===>you can make very small triangle whose perimeter is  less than 1. 
hence statement 1 is not sufficient.

STATEMENT 2: 
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.
hence B

HOPE IT HELPS

Bunuel · Answer

Is the perimeter of a triangle greater than 1? (1) Two of the heights are less than 1/3. Well, we can have a tiny triangle with the perimeter less than 1 but we also can have a right triangle with legs (heights) bit less than 1/3 = 0.(3). In this case hypotenuse wold be a bit less than 0.47 and the perimeter would be more than 1. Not sufficient. (2) One of the heights is greater than 1/2. Consider the easiest case: https://gmatclub.com/forum/download/file.php?id=20521 AB > 1/2, BC = hypotenuse > AB, thus the perimeter is for sure greater than 1. Sufficient. Answer: B. Hope it's clear. Perimeter2.png

bumpbot · Answer

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Is the perimeter of a triangle greater than 1?

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