I believe that the problem should read as follows:
Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?
I. 3
II. 9√3
III. 13.5
I only
II only
III only
II and III
I, II and III
THIRD SIDE RULE:
The "third side" of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference between the lengths of the other two sides.
Since AC=6 and BC=9, we get the following range for AB:
9-6 < AB < 9+6
3 < AB < 15.
Since 9√3 ≈ (9)(1.7) = 15.3, only Statement III is a possible length for AB.
The correct answer is
C.
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