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Anastasy [175]
2 years ago
15

If the sides of a triangle have the following lengths, AB = 2x + 5, BC = 3x-2 and AC = 4x - 8, find all the possible values of x

.
Mathematics
1 answer:
katovenus [111]2 years ago
5 0

9514 1404 393

Answer:

  x > 3

Step-by-step explanation:

The triangle inequality requires ...

<u>AB +BC > AC</u>

  (2x +5) +(3x -2) > (4x -8)

  5x +3 > 4x -8

  x > -11

<u>BC +AC > AB</u>

  (3x -2) +(4x -8) > (2x +5)

  7x -10 > 2x +5

  5x > 15

  x > 3

<u>AC +AB > BC</u>

  (4x -8) +(2x +5) > (3x -2)

  6x -3 > 3x -2

  3x > 1

  x > 1/3

The most restrictive of these conditions on x is ...

  x > 3 . . . . all possible values of x

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