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If each of the sides of a triangle satisfies the equation x2+18=9x ,

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rukna
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If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   09 Apr 2016, 06:27
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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.
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B
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chetan2u
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   09 Apr 2016, 07:45
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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
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   09 Apr 2016, 22:57
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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 :)

Thanks for explaining.
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If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   Updated on: 18 Sep 2017, 04:18
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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 any side of a triangle satisfies..."?

Originally posted by alainca on 01 Sep 2017, 05:03.
Last edited by alainca on 18 Sep 2017, 04:18, edited 2 times in total.
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   14 Nov 2017, 02:51
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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


And I thought that here "x" represents the x-coordinate of the vertices! Damn I don't know wat I was thinking. But it should be specified that x represents the length of each sides.
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   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?
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   09 May 2017, 20:11
Expert Reply
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?


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] New post   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
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   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] New post   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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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   01 Aug 2020, 06:55
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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.


Solution:

Let’s solve the given equation:

x^2 - 9x + 18 = 0

(x - 6)(x - 3) = 0

x = 6 or x = 3

If all the sides are 3, then the perimeter is 9. If all the sides are 6, then the perimeter is 18. If two sides are 6 and the third side is 3, then the perimeter is 15. However, it’s not possible that two sides are 3 and the third side is 6 since the sum of any two sides of a triangle must be greater than the third side, but 3 + 3 is not greater than 6. Therefore, the perimeter can’t be 12.

Answer: B
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   30 Jan 2022, 07:32
Official Explanation:

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. Consider each answer choice to see if it is possible given that restriction on the sides:

(A) POSSIBLE - the triangle could be 3-3-3 (B) NOT POSSIBLE - the triangle cannot be 3-3-6 as this violates the third side rule - remember that the two shorter sides must have a sum greater than the length of the longest side! (C) POSSIBLE - the triangle could be 6-6-3 (D) POSSIBLE - the triangle could be 6-6-6 (E) INCORRECT

Since you need the one answer that is not possible, (B) is correct.
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink] New post   18 Nov 2023, 00:55
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , [#permalink]
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