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Reptile [31]
2 years ago
9

Find all possible values of x if these represent side of a triangle 2x,5-x,4

Mathematics
1 answer:
3241004551 [841]2 years ago
7 0

Answer:

  • -1/3 < x < 3 or x = (-1/3, 3)

Step-by-step explanation:

<u>Given sides of a triangle:</u>

  • 2x, 5 - x, 4

<u>Triangle inequality theorem:</u>

  • Any side is smaller than the some of the other two.

<u>Apply to the given triangle:</u>

  • 2x + 5 - x > 4 ⇒ x > -1
  • 2x + 4 > 5 - x ⇒ 3x > -1 ⇒ x > -1/3
  • 5 - x + 4 > 2x ⇒ 3x < 9 ⇒ x < 3

<u>Combine all the inequalities:</u>

  • -1/3 < x < 3
  • x = (-1/3, 3)
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