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If each of the sides of a triangle satisfies the equation :- x^2+18=9x

then the perimeter of the triangle CANNOT be:

A. 9 B. 12 C. 15 D. 18 E. Any of the four values above is possible.

For some reason, I find the fault in question. Can someone please explain. Posted official answer.

HI, each side satisfies\(x^2+18=9x\) \(x^2-9x+18=0\).. \((x-3)(x-6)=0\).. so x=3 or x=6.. so sides can be 3 or 6... If all 3, P= 9 if all 6, P = 18 If two sides 6 and third side 3= 2*6+3=15 If two sides 3 and third side 6, P= 2*3+6=12.. BUT is this possible?.. NO,the sum of two sides which are 3 is EQUAL to third side.. so TRIANGLE is not possible, it will be just a straight line measuring 6.. so 12 is not possible ans B
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink]

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09 Apr 2016, 22:57

Thanks. I can't believe what silly mistake I did. if you practice only 700 level question, your mind sometimes get screwed and you start finding something strange even in basic questions

Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink]

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01 May 2017, 03:38

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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink]

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09 May 2017, 19:55

chetan2u wrote:

rukna wrote:

If each of the sides of a triangle satisfies the equation :- x^2+18=9x

then the perimeter of the triangle CANNOT be:

A. 9 B. 12 C. 15 D. 18 E. Any of the four values above is possible.

For some reason, I find the fault in question. Can someone please explain. Posted official answer.

HI, each side satisfies\(x^2+18=9x\) \(x^2-9x+18=0\).. \((x-3)(x-6)=0\).. so x=3 or x=6.. so sides can be 3 or 6... If all 3, P= 9 if all 6, P = 18 If two sides 6 and third side 3= 2*6+3=15 If two sides 3 and third side 6, P= 2*3+6=12.. BUT is this possible?.. NO,the sum of two sides which are 3 is EQUAL to third side.. so TRIANGLE is not possible, it will be just a straight line measuring 6.. so 12 is not possible ans B

Could you plz explain the part highlighted in blue? As to why if the sum of 2 sides is equal to the 3rd,then it cannot be a triangle?

If each of the sides of a triangle satisfies the equation :- x^2+18=9x

then the perimeter of the triangle CANNOT be:

A. 9 B. 12 C. 15 D. 18 E. Any of the four values above is possible.

For some reason, I find the fault in question. Can someone please explain. Posted official answer.

HI, each side satisfies\(x^2+18=9x\) \(x^2-9x+18=0\).. \((x-3)(x-6)=0\).. so x=3 or x=6.. so sides can be 3 or 6... If all 3, P= 9 if all 6, P = 18 If two sides 6 and third side 3= 2*6+3=15 If two sides 3 and third side 6, P= 2*3+6=12.. BUT is this possible?.. NO,the sum of two sides which are 3 is EQUAL to third side.. so TRIANGLE is not possible, it will be just a straight line measuring 6.. so 12 is not possible ans B

Could you plz explain the part highlighted in blue? As to why if the sum of 2 sides is equal to the 3rd,then it cannot be a triangle?

Hi, If two sides are 3 and third side is 6....AB =BC=3... So the third side AC has to be less than AB+BC or 6 because than only Point B will make an angle. When it is 6, it means AC is a straight line and B is the midpoint of the line.
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink]

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04 Jul 2017, 09:52

ishitam wrote:

chetan2u wrote:

rukna wrote:

If each of the sides of a triangle satisfies the equation :- x^2+18=9x

then the perimeter of the triangle CANNOT be:

A. 9 B. 12 C. 15 D. 18 E. Any of the four values above is possible.

For some reason, I find the fault in question. Can someone please explain. Posted official answer.

HI, each side satisfies\(x^2+18=9x\) \(x^2-9x+18=0\).. \((x-3)(x-6)=0\).. so x=3 or x=6.. so sides can be 3 or 6... If all 3, P= 9 if all 6, P = 18 If two sides 6 and third side 3= 2*6+3=15 If two sides 3 and third side 6, P= 2*3+6=12.. BUT is this possible?.. NO,the sum of two sides which are 3 is EQUAL to third side.. so TRIANGLE is not possible, it will be just a straight line measuring 6.. so 12 is not possible ans B

Could you plz explain the part highlighted in blue? As to why if the sum of 2 sides is equal to the 3rd,then it cannot be a triangle?

Learn a basic and very important rule:

For a triangle, Difference of other two sides < third side < sum of other two sides

Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink]

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10 Sep 2017, 03:08

rukna wrote:

If each of the sides of a triangle satisfies the equation x^2+18=9x, the perimeter of the triangle CANNOT be:

(A) 9 (B) 12 (C) 15 (D) 18 (E) Any of the four values above is possible.

If x² - 9x + 18 = 0, then (x - 3)(x - 6) = 0 and x = 3 or x = 6, so each side of the triangle is 3 or 6. A 3-3-6 triangle violates our law of triangles, however: remember that the two shorter sides must have a sum greater than the length of the longest side!
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink]

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17 Sep 2017, 20:19

alainca Agreed! The wording is super ambiguous. Are real GMAT questions like this? or is it just veritas prep questions that are frequently ambiguous??

alainca wrote:

rukna wrote:

If each of the sides of a triangle satisfies the equation:- x^2+18=9x.

Could this be reworded better? I don't think that a "side" satisfies an equation. The length of a side can satisfy an equation. How about

"If the length x of each side of a triangle satisfies..."?

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