Question

27

C
A
54
B
Based on the diagram, which expresses all possible
lengths of segment AB?
O AB = 25
O 27 OAB = 85
O AB< 27 or AB > 81

Answer 1

B. 27 < AB < 81

Explanation:

The triangle inequality requires that the length of any given side of a triangle be greater than the difference and less than the sum of the other two sides.

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application

54 -27 < AB < 54 +27

27 < AB < 81

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Additional comment

Some versions of the triangle inequality allow the "or equal to" case.

27 ≤ AB ≤ 81

Apparently, the one used here does not.

If the sum of the two short sides is equal to the long side, the "triangle" looks like a line segment. Its altitude and area are zero.