High School

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Given a triangle with sides labeled as 7, x, and 5, use the triangle to write three inequalities:

1. \( 7 + 5 > x \)
2. \( 7 + x > 5 \)
3. \( x + 5 > 7 \)

Answer :

Final answer:

Set up three inequalities from the given triangle with sides 7, x, and 5 using the triangle inequality theorem, which are 7 + x > 5, x + 5 > 7, and 7 + 5 > x.

Explanation:

The given triangle has sides of lengths 7, x, and 5. To write the three inequalities using the Triangle Inequality theorem, which states that the sum of the lengths of any two sides of a triangle should be greater than the length of the third side:

  1. 7 + x > 5. This expresses that the sum of the lengths of sides 7 and x is greater than 5.
  2. 7 + 5 > x. This shows that the sum of the lengths of sides 7 and 5 should be greater than side x.
  3. x + 5 > 7. This communicates that the sum of the lengths of sides x and 5 surpasses 7.

Learn more about Triangle Inequality here:

https://brainly.com/question/37190402

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