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In any triangle, the sum of two sides is greater than twice the median to the third side. In triangle ABC, AB = 8 and AC = 6. The median AD to BC satisfies which bound?

Class 9Inequalities in a TriangleGeometry — Triangles
  • AAD < 7
  • BAD < 14
  • CAD > 7
  • DAD = 7

Step-by-Step Solution

Property: AB + AC > 2*AD (the median to BC). So 8 + 6 = 14 > 2*AD, giving AD < 7.
Answer: A) AD < 7

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