Question

Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.

Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81

Answer 1

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Answer 2

27 < AB < 81

Explanation:

By the triangle inequality theorem,

If CB is the longest, AB + 27 > 54, meaning AB > 27.

If AB is the longest, 27 + 54 < AB, meaning 81 < AB.

Thus, 27 < AB < 81