a, b, c - sides of a triangle
Therefore:
a + b > c
a + c > b
b + c > a
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We have a = AB, b = 140mi, c = 100mi.
(1) a + b > c
AB + 140 > 100 subtract 140 from both sides
AB > -40 → AB > 0
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(2) a + c > b
AB + 100 > 140 subtract 100 from both sides
AB > 40
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(3) b + c > a → a < b + c
AB < 140 + 100
AB < 240
Answer: 40 < AB < 240