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

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

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. _________________

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

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

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.

let me update: I mean "a side with 1/2 length makes the sum of other two sides at least > than 1/2, making P greater than 1". right?

Re: Is the perimeter of a triangle greater than 1? 1). Two of [#permalink]
11 Jul 2013, 10:54

2

This post received KUDOS

veenu08 wrote:

can someone please explain the logic for this question

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

Attachments

tri.jpg [ 3.51 KiB | Viewed 1820 times ]

STMN 1.png [ 8.83 KiB | Viewed 1819 times ]

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Re: Is the perimeter of a triangle greater than 1? 1). Two of [#permalink]
11 Jul 2013, 11:10

Expert's post

1

This post was BOOKMARKED

veenu08 wrote:

can someone please explain the logic for this question

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:

Attachment:

Perimeter2.png [ 2.22 KiB | Viewed 1816 times ]

AB>1/2, BC=hypotenuse>AB, thus the perimeter is for sure greater than 1. Sufficient.

Re: Is the perimeter of a triangle greater than 1? [#permalink]
10 Dec 2013, 04:34

So in other words, you can take the height (less than 1/3 of the triangle) then take the height of the triangle formed by the new triangle (where the height is less than 1/3?) I guess there is nothing implying otherwise, but I didn't think it would count to take the height of one triangle and then another one formed inside that triangle.

Re: Is the perimeter of a triangle greater than 1? [#permalink]
09 Aug 2015, 22:37

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