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# triangle A has one side of lenght x. if x^4=81 what is the

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Manager
Joined: 11 Feb 2011
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triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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08 May 2011, 05:39
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55% (hard)

Question Stats:

53% (01:18) correct 47% (01:25) wrong based on 342 sessions

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triangle A has one side of lenght x. if x^4=81 what is the perimeter of triangle A?
1.Triangle A has sides whose lengths are consecutive integers
2.Triangle A is not a right triangle.

What i want to know is what exactly does it mean to say Triangle A is not a Rt triangle in context to question above,It is not making sense to me.

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08 May 2011, 06:04
1

S1 says that the sides are consecutive integers and one of the side is 4. There can be three possibilities
3,4,5
2,3,4
1,2,3
Clearly insufficient

S2 says that triangle A is not a right angle. I still have two cases i.e. 2,3,4 and 1,2,3. Clearly insufficient

Combining 1) and 2) two cases are left. Answer E

PS : I think the question is not making any sense. It something like - the values of a,b,c are given and suddenly the question is asking x+y+z

AnkitK wrote:
triangle A has one side of lenght x. if x^4=81 what is the perimeter of triangle A?
1.Triangle A has sides whose lengths are consecutive integers
2.Triangle A is not a right triangle.

What i want to know is what exactly does it mean to say Triangle A is not a Rt triangle in context to question above,It is not making sense to me.
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 654

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08 May 2011, 06:30
1
Damn missed the checks ! Thanks fluke !

fluke wrote:
gmat1220 wrote:

S1 says that the sides are consecutive integers and one of the side is 4. There can be three possibilities
3,4,5(It is a pythagorean triplet and must be a right angle triangle)
2,3,4(It is a NOT pythagorean triplet 2^2+3^2 != 4^2 and must NOT be a right angle triangle)
1,2,3(Not possible because sum of two sides is equal to the third)
Clearly insufficient

S2 says that triangle A is not a right angle. I still have two cases i.e. 2,3,4 and 1,2,3. Clearly insufficient

Combining 1) and 2) two cases are left(Just one case: 2,3,4). Answer E(C)

PS : I think the question is not making any sense. It something like - the values of a,b,c are given and suddenly the question is asking x+y+z

AnkitK wrote:
triangle A has one side of lenght x. if x^4=81 what is the perimeter of triangle A?
1.Triangle A has sides whose lengths are consecutive integers
2.Triangle A is not a right triangle.

What i want to know is what exactly does it mean to say Triangle A is not a Rt triangle in context to question above,It is not making sense to me.
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08 May 2011, 06:44
1
x = 3

(1)

So 2 possible triplets

3,4,5

2,3,4

1,2,3 is not possible as 2 = 3-1

Insufficient

(2)

Insufficient

(1) + (2)

It's not a pythagorean triplet from (2)

so 2,3,4

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08 May 2011, 08:42
1
Concept: If a,b,c are the measurements of 3 sides of a triangle. Then measurement of b will be considering a<b<c

c-a < b < c+b .

Since x = 3

a gives 2,3,4 and 3,4,5. Not sufficient.

b still the sides can be 3,5,7 or 2,3,4 etc. Not sufficient.

a+b means 3,4,5 is not the measurements.It is 2,3,4.

Hence C.
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08 May 2011, 17:18
1. Not sufficient

as the sides could be anyone of this combination 3,4,5 or 2,3,4

2. Not sufficient
not a right angled triangle

together we can eliminate the 2,3,4

Sufficient

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Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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18 Jul 2016, 00:33
C

x=3(given)
1) three possibilities:
1,2,3(this is not a possible triangle as 1+2=3 not >3)
2,3,4
3,4,5(right angled)

2)not a right angled.insuff ok its not right angled..but we ddont know other 2 sides

1+2

only one case 2,3,4

so ans is C
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Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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17 Aug 2016, 08:46
so if it i s 2-3-4 pair, what is the area? 2*3/ 2 ? Bunuel can you help?
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Joined: 29 Jun 2016
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Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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17 Aug 2016, 09:42
alpham wrote:
so if it i s 2-3-4 pair, what is the area? 2*3/ 2 ? Bunuel can you help?

It is not a right angled triangle so we cannot use it directly
Instead when three sides of a triangle are known
the area of a triangle whose sides have lengths a, b, and c is

the area pf a trainagle A = sqrt{s(s-a)(s-b)(s-c)},
where s is the semiperimeter of the triangle; that is,
s=(a+b+c)/2
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Joined: 29 Jun 2016
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Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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17 Aug 2016, 09:44
in this case as s=9/2
Area=sqrt(9/2*5*2*3/2*1/2)
=3/4*sqrt(15)
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Joined: 23 Jul 2015
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Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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05 Jan 2017, 01:44
AnkitK wrote:
triangle A has one side of lenght x. if x^4=81 what is the perimeter of triangle A?
1.Triangle A has sides whose lengths are consecutive integers
2.Triangle A is not a right triangle.

What i want to know is what exactly does it mean to say Triangle A is not a Rt triangle in context to question above,It is not making sense to me.

$$x^4$$ = 81 --> x=3

stmt 1 - two possibilities {2,3,4} or {3,4,5} --> Insuff.
stmt 2 - Many possibilities --> Insuff

1 &2 only {2,3,4} possible --> Suff --> Ans is C
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Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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22 Oct 2018, 07:15
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Re: triangle A has one side of lenght x. if x^4=81 what is the   [#permalink] 22 Oct 2018, 07:15
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