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KVPY2012MathematicsSequences and Series

The sides of a triangle are distinct positive integers in an arithmetic progression. If the smallest side is 10 , the number of such triangles is -

Options

  1. A8
  2. B9
  3. C10
  4. DInfinitely many

Correct answer

B. 9

Step-by-step solution

as a, b, c are an AP so 10,10+ d , 10+2 ~d sum of a+b>c array l 20+ d >10+2 ~d 10> d array As the d is minimum, Hence total possibility of d is 9

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