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Two villages A and B are 15 km apart. A water tank T is to be built so that TA = 9 km.
If T must form a triangle with A and B, between what two values (exclusive) must TB lie?

Class 9Inequalities in a TriangleGeometry — Triangles
  • Abetween 6 km and 24 km
  • Bbetween 9 km and 15 km
  • Cbetween 0 km and 15 km
  • Dbetween 6 km and 15 km

Step-by-Step Solution

TB must satisfy |15 - 9| < TB < 15 + 9, i.e. 6 < TB < 24. So TB lies strictly between 6 km and 24 km.
Answer: A) between 6 km and 24 km

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