Question

Given triangle ABC with sides AB = 3x + 4 , BC = 2x + 5 , and AC = 4x , determine the values of x such that triangle ABC exists

Answer 1

Answer:

  x > 1/5

Step-by-step explanation:

All of these three triangle inequalities must be satisfied:

  AB +BC > AC

  BC +CA > BA

  CA +AB > CB

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Taking these one at a time, we have ...

  AB +BC > AC

  3x +4 + 2x +5 > 4x

  x +9 > 0 . . . . . subtract 4x

  x > -9

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  BC +CA > BA

  2x +5 + 4x > 3x +4

  3x > -1 . . . . . . subtract 3x+5

  x > -1/3 . . . . . divide by 3

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  CA + AB > CB

  4x + 3x +4 > 2x +5

  5x > 1 . . . . . . subtract 2x+4

  x > 1/5

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The only values of x that satisfy all of these inequalities are those such that ...

  x > 1/5