Valid triangle side lengths

CMAT 2020 · Quantitative Techniques & Data Interpretation · Easy · Geometry

Which of the following sets of numbers can be used as the lengths of the sides of a triangle ?

  1. A.

    [5, 7, 12]

  2. B.

    [5, 7, 9]

  3. C.

    [7, 9, 17]

  4. D.

    [2, 4, 10]

Answer

B

Explanation

By triangle inequality, the sum of any two sides must be strictly greater than the third side.

  • [5,7,12][5, 7, 12]: 5+7=12≯125 + 7 = 12 \ngtr 12
  • [5,7,9][5, 7, 9]: 5+7=12>95 + 7 = 12 > 9, 5+9=14>75 + 9 = 14 > 7, 7+9=16>57 + 9 = 16 > 5 (Valid)
  • [7,9,17][7, 9, 17]: 7+9=16≯177 + 9 = 16 \ngtr 17
  • [2,4,10][2, 4, 10]: 2+4=6≯102 + 4 = 6 \ngtr 10

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