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Three towns Patna, Gaya and Ranchi form a triangle. Patna-Gaya = 100 km and Gaya-Ranchi = 250 km.
A cyclist claims Patna-Ranchi could be exactly 150 km. Is a triangle possible with these three distances?

Class 9Inequalities in a TriangleGeometry — Triangles
  • ANo, because 100 + 150 = 250 (degenerate)
  • BYes, it is a valid triangle
  • CYes, it is a right triangle
  • DNo, because 250 - 100 = 150 only by chance

Step-by-Step Solution

The two smaller distances 100 and 150 sum to 250, equal to the third. Since the sum is not strictly greater, the three points are collinear (degenerate) and no proper triangle is formed.
Answer: A) No, because 100 + 150 = 250 (degenerate)

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