In a quadrilateral ABCD, AB = 6 cm, BC = 18 cm, CD = 6 cm and DA = 10 cm. If the diagonal BD = x, then which one of the following is correct?
A.8 < x < 12
B.12 < x < 16✓ Correct
C.16 < x < 18
D.18 < x < 20
Explanation
In triangle ABD: |AB - DA| < BD < AB + DA, so |6 - 10| < x < 16, i.e., 4 < x < 16. In triangle BCD: |BC - CD| < BD < BC + CD, so |18 - 6| < x < 24, i.e., 12 < x < 24. Intersection: 12 < x < 16.
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