Bunuel wrote:
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
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
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