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Which set of three lengths can form a valid triangle for which Heron's formula gives a real area?

Class 9Area of a Triangle by Heron's FormulaMensuration
  • A5 cm, 6 cm, 9 cm
  • B2 cm, 3 cm, 8 cm
  • C1 cm, 1 cm, 5 cm
  • D4 cm, 5 cm, 9 cm

Step-by-Step Solution

A triangle needs the sum of any two sides greater than the third. Only 5+6 > 9 holds (5+6=11>9); the others fail (e.g. 4+5=9 is degenerate).
Answer: A) 5 cm, 6 cm, 9 cm

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