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

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AnkitK
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triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   08 May 2011, 05:39
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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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C
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Re: triangles! [#permalink] New post   08 May 2011, 06:04
The answer is E.

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. :o 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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Re: triangles! [#permalink] New post   08 May 2011, 06:30
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Damn missed the checks ! Thanks fluke !

fluke wrote:
gmat1220 wrote:
The answer is E.

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. :o 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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Re: triangles! [#permalink] New post   08 May 2011, 06:44
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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

Answer - C
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Re: triangles! [#permalink] New post   08 May 2011, 08:42
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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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Re: triangles! [#permalink] New post   08 May 2011, 17:18
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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

Answer is C.
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Re: triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   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] New post   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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Re: triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   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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Re: triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   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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Re: triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   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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triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   Updated on: 03 Nov 2019, 08:47
I'm seeing answers that treat {2,3,4} & {3,4,5} as the only possibilities, but nowhere in the question does it mention that the lengths of the triangle have to be integers. Could someone clarify why then we can't consider triangles such as {2.1,3,3.5}...?

Sorry. My bad. Did not notice the word "integer" in Statement 1.

Originally posted by lumocolor on 02 Nov 2019, 21:48.
Last edited by lumocolor on 03 Nov 2019, 08:47, edited 1 time in total.
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Re: triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   02 Nov 2019, 23:41
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.



It is given that x=3 and perimeter is to be calculated

(1) possible triangles are
2,3,4 or 3,4,5 . Insufficient

(2) Triangle is not right angles. No further information. Insufficient

(1)+(2) triangle 3,4,5 is not possible. Only triangle 2,3,4 is possible. sufficient

C is correct.
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Re: triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   17 Nov 2019, 07:24
can you show calculation on how we reached at 3
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Re: triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   09 Oct 2020, 12:23
chavi wrote:
can you show calculation on how we reached at 3

Root over (x^8) = 81
x^(8/2) = 81
x^4 = 81
x = 3
This is the way x=3 can be found.
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Re: triangle A has one side of lenght x. if x^4=81 what is the [#permalink] New post   20 Aug 2021, 12:16
[quote="gmat1220"]The answer is E.

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. :o It something like - the values of a,b,c are given and suddenly the question is asking x+y+z


How did we exclude 1,2,3 as a possibility
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Re: triangle A has one side of lenght x. if x^4=81 what is the [#permalink]
20 Aug 2021, 12:16
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Bunuel
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