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Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s [#permalink]

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04 May 2017, 18:08

ziyuen wrote:

Is \(a+b>c\)?

(1) a, b, and c represent three different lengths of the sides of a certain triangle

(2) \(a^2+b^2=c^2\)

OFFICIAL EXPLANATION

According to the characteristics of a certain triangle, if you let a, b, and c represent the 3 different side lengths of a triangle, \(a-b<c<a+b\) appears often.

In other words, the sum of the lengths of the two sides is longer than the length of the other side.

(1) The condition is always yes. Sufficient.

(2) It is not about the Pythagorean Theorem of a right triangle. If (a,b,c)=(3,4,5), it is yes, but if (-3,-4,5), it is no. Insufficient.

Bunuel & MathRevolution Could the side of a triangle be negative value?
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"Be challenged at EVERY MOMENT."

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Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s [#permalink]

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04 May 2017, 18:24

ziyuen wrote:

ziyuen wrote:

Is \(a+b>c\)?

(1) a, b, and c represent three different lengths of the sides of a certain triangle

(2) \(a^2+b^2=c^2\)

OFFICIAL EXPLANATION

According to the characteristics of a certain triangle, if you let a, b, and c represent the 3 different side lengths of a triangle, \(a-b<c<a+b\) appears often.

In other words, the sum of the lengths of the two sides is longer than the length of the other side.

(1) The condition is always yes. Sufficient.

(2) It is not about the Pythagorean Theorem of a right triangle. If (a,b,c)=(3,4,5), it is yes, but if (-3,-4,5), it is no. Insufficient.

but for the instance, please let me know from where u r assuming the option 2 relates to any triangle?? a,b,c are independent values and they are not meant for any triangle

Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s [#permalink]

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04 May 2017, 18:55

rohit8865 wrote:

ziyuen wrote:

ziyuen wrote:

Is \(a+b>c\)?

(1) a, b, and c represent three different lengths of the sides of a certain triangle

(2) \(a^2+b^2=c^2\)

OFFICIAL EXPLANATION

According to the characteristics of a certain triangle, if you let a, b, and c represent the 3 different side lengths of a triangle, \(a-b<c<a+b\) appears often.

In other words, the sum of the lengths of the two sides is longer than the length of the other side.

(1) The condition is always yes. Sufficient.

(2) It is not about the Pythagorean Theorem of a right triangle. If (a,b,c)=(3,4,5), it is yes, but if (-3,-4,5), it is no. Insufficient.

but for the instance, please let me know from where u r assuming the option 2 relates to any triangle?? a,b,c are independent values and they are not meant for any triangle

• A Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\), such that \(a^2 + b^2 = c^2\). Such a triple is commonly written \((a, b, c)\), and a well-known example is \((3, 4, 5)\). If \((a, b, c)\) is a Pythagorean triple, then so is \((ka, kb, kc)\) for any positive integer \(k\). There are 16 primitive Pythagorean triples with c ≤ 100: (3, 4, 5)(5, 12, 13)(7, 24, 25)(8, 15, 17) (9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65) (36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97).
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"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

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Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s [#permalink]

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05 Oct 2017, 18:44

ishitam wrote:

rohit8865 wrote:

AustinKL wrote:

Is \(a+b>c\)?

1) a, b, and c represent three different lengths of the sides of a certain triangle

2) \(a^2+b^2=c^2\)

(1) sum of any two sides of triangle is always> third side......suff

(2) if a= 3 , b= 4 and c= 5 ...Yes if a= 3 , b= -4 and c= 5 ...No insuff

Ans A

How can the side of a triangle be negative?

ishitam , Please consider the 2nd statement, independently, as just another algebraic equation. Yes it does represent Pythagoras theorem, but there is no where mentioned that a, b,c are sides of triangle in question stem. 2nd is a classic trap statement, wherein we do not completely remove the context given in statement 1 and assume something which is not present in statement 2.

Is a+b>c? 1) a, b, and c represent three different lengths of the s [#permalink]

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30 Nov 2017, 13:34

a+b > c?

Statement 1: Property of a triangle, sum of any two sides is greater than the third side, hence a + b > c, sufficient

Statement 2: if a, b, c -> pythogorian triplet, say {a = 3, b = 4, c = 5}, then a + b > c, if a = 0, b = 0, c = 0, then \(a^2 + b^2 = c^2\), but a +b = c, not sufficient