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In triangle ABC, the length of side AB is 12 inches and the length of side BC is 19 inches. Which of the following could be the length of side AC?

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Final answer:

To determine the possible length of side AC in triangle ABC, apply the Triangle Inequality Theorem, stating that the possible length of AC must be greater than 7 inches and less than 31 inches.

Step-by-step explanation:

The question concerns determining the possible length of the third side of a triangle given the lengths of the other two sides. This is a problem in Geometry, which can be approached by using the Triangle Inequality Theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

In the case of triangle ABC, with side lengths AB = 12 inches and BC = 19 inches, the possible length of side AC must be greater than the difference of AB and BC, and less than their sum:

  • AC > BC - AB | 19 - 12 = 7 inches
  • AC < AB + BC | 12 + 19 = 31 inches

Therefore, a possible length for side AC could be any value greater than 7 inches and less than 31 inches, for example, 18 inches.

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