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If x>0, and two sides of a certain triangle
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30 Aug 2016, 02:20
30 Aug 2016, 02:20
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Question Stats:
30% (01:42) correct
69% (01:30) wrong based on 184 sessions
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If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle?
Indicate all possible lengths.
A) 4x+5
B) x+2
C) 6x+1
D) 5x+6
E) 2x+17
Indicate all possible lengths.
A) 4x+5
B) x+2
C) 6x+1
D) 5x+6
E) 2x+17
Re: If x>0, and two sides of a certain triangle
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30 Aug 2016, 05:10
30 Aug 2016, 05:10
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Let the third side be y
then (3x + 4) – (2x + 1) < y < (3x + 4) + (2x + 1)
=> x + 3 < y < 5x + 5
As with option B, x+2 is always less than x+3, therefore B is not possible.
And with option E, if we choose x=5, then 2x+17= 27
=> from inequality, 8<27<30
Hope, the solution is clear!
then (3x + 4) – (2x + 1) < y < (3x + 4) + (2x + 1)
=> x + 3 < y < 5x + 5
As with option B, x+2 is always less than x+3, therefore B is not possible.
And with option E, if we choose x=5, then 2x+17= 27
=> from inequality, 8<27<30
Hope, the solution is clear!
General Discussion
Re: If x>0, and two sides of a certain triangle
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30 Aug 2016, 04:35
30 Aug 2016, 04:35
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Expert Reply
Hi,
I think B should be one of the solutions too
Let the triangle have side named A, B and C
A= 2x+1 and B= 3x+4
A+B= 5x+5
Now we know from triangle inequality
C < A +B
Option A
4x+5 < 5x+5
=>x > 0
Option B
x +2 < 5x+5
=> -4x < 3 => x > \(\frac{-3}{4}\).
There is also possible as long as x >0 it is also x > \(\frac{-3}{4}\)
Option C
6x+1 < 5x+5
x < 4
Also a possible solution exits such that 0 < x < 4.
Option D is not possible.
Option E is also similarly possible.
I think B should be one of the solutions too
Let the triangle have side named A, B and C
A= 2x+1 and B= 3x+4
A+B= 5x+5
Now we know from triangle inequality
C < A +B
Option A
4x+5 < 5x+5
=>x > 0
Option B
x +2 < 5x+5
=> -4x < 3 => x > \(\frac{-3}{4}\).
There is also possible as long as x >0 it is also x > \(\frac{-3}{4}\)
Option C
6x+1 < 5x+5
x < 4
Also a possible solution exits such that 0 < x < 4.
Option D is not possible.
Option E is also similarly possible.
