Question:

If the largest side of a triangle is \( A \), and the other two sides are \( B \) and \( C \), what relation exists between them?

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The triangle inequality theorem helps to determine the possible relationships between the sides of a triangle.
Updated On: Sep 30, 2025
  • \( A = B + C \)
  • \( A + C \)
  • \( A>|B - C| \)
  • \( |B - C| \)
  • \( A - \pi(B - C) \)
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The Correct Option is C

Solution and Explanation

Step 1: Recall the triangle inequality theorem.
In any triangle, the sum of the lengths of any two sides must always be greater than the length of the third side. This is known as the triangle inequality theorem: \[ A<B + C, \quad B<A + C, \quad C<A + B. \]
Step 2: Conclusion.
The correct relationship is: \[ A>|B - C|. \]
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