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# Is the perimeter of a triangle greater than 1? 1). Two of

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Is the perimeter of a triangle greater than 1? 1). Two of [#permalink]  10 Jun 2006, 21:59
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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
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B it is
(1) is insufficient to decide whether Per > 1 or not
(2) One height >1/2 so we have at least two sides > 1/2
so the perimeter>1
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Re: DS - Geomerty [#permalink]  11 Jun 2006, 11:03
gmat_crack 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

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

Last edited by Professor on 11 Jun 2006, 12:05, edited 1 time in total.
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D. Either stmt is sufficient

Stmt1 Analysis:

If a,b,c are the three sides and h1 and h2 are the two heights (lets say h1 divides b into b' and b", and h2 divides c into c' and c".

h1 > 1/3, h2 > 1/3
(a+b') > h1
(a+b') > 1/3 ... (a)

(c+b") > h1
(c+b") > 1/3.... (b)

(a+c+b'+b") > 2/3

(a+b+c) > 2/3 which is less than 1.

Same can be done for h2.

Stmt1 is sufficient.

Stmt2 Analysis:

Using the same method as above for one height h > 1/2,

We can arrive @ (a+b+c) > 1

Stmt2 is sufficient.

Therefore D.
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Re: DS - Geomerty [#permalink]  11 Jun 2006, 11:21
Professor wrote:
gmat_crack 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

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.

Note that we just have to answer if (a+b+c)>1 or not.

Stmt 1 says it is not, stmt2 says it is. So separately both answer the question.

So, I think it should be D.
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Re: DS - Geomerty [#permalink]  11 Jun 2006, 11:26
Professor wrote:
gmat_crack 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

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.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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Re: DS - Geomerty [#permalink]  11 Jun 2006, 12:03
haas_mba07 wrote:
Professor wrote:
gmat_crack 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

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

Note that we just have to answer if (a+b+c)>1 or not.

Stmt 1 says it is not, stmt2 says it is. So separately both answer the question.

So, I think it should be D.

A is not suff. it doesnot tell about the third side.

if s1=0.32, s2=0.32 and s3 = 0.6, Perimeter is >1.
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Re: DS - Geomerty [#permalink]  11 Jun 2006, 12:13
ps_dahiya wrote:
Professor wrote:
gmat_crack 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

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: DS - Geomerty   [#permalink] 11 Jun 2006, 12:13
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