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22 May 2020, 06:52
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D
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Difficulty:
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Question Stats:
85% (00:36) correct
15%
(01:18)
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based on 138
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Which of the following describes all values of x such that there is a triangle with sides having lengths 3, 4, and x ?
A. 5 < x < 12
B. 4 < x < 7
C. 3 < x < 5
D. 1 < x < 7
E. 1 < x < 4
PS21256
A. 5 < x < 12
B. 4 < x < 7
C. 3 < x < 5
D. 1 < x < 7
E. 1 < x < 4
PS21256
22 May 2020, 06:56
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Bunuel
Which of the following describes all values of x such that there is a triangle with sides having lengths 3, 4, and x ?
A. 5 < x < 12
B. 4 < x < 7
C. 3 < x < 5
D. 1 < x < 7
E. 1 < x < 4
PS21256
A. 5 < x < 12
B. 4 < x < 7
C. 3 < x < 5
D. 1 < x < 7
E. 1 < x < 4
PS21256
Property: FOr a triangle to exist, Sum if any two sides must be GREATER than third side
i.e. FOr \(x_{min}\), 3+x > 4
i.e. \(x_{min} > 1\)
i.e. FOr \(x_{max}\), 3+4 > x
i.e. \(x_{max} < 7\)
i.e. 1 < x < 7
Answer: Option D
General Discussion
22 May 2020, 11:05
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Any side of a triangle is always between the (absolute sum and the absolute difference of the other two sides), exclusive.
|4 - 3| < x < |4 + 3|
So, 1 < x <7, Option D
|4 - 3| < x < |4 + 3|
So, 1 < x <7, Option D
