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  # Sides of Quadrilateral | PRMO 2017 | Question 20
  
  Try this beautiful problem from the Pre-RMO, 2017 based on Sides of Quadrilateral.
  
  ## Sides of Quadrilateral - PRMO 2017
  
  What is the number of triples (a,b,c) of positive integers such that (i) a<b<c<10 and (ii) a,b,c,10 form the sides of a quadrilateral?
  
  • is 107
  • is 73
  • is 840
  • cannot be determined from the given information
  
  ### Key Concepts
  
  Largest number of triples
  
  Distance
  
  ## Check the Answer
  
  PRMO, 2017, Question 20
  
  Geometry Vol I to IV by Hall and Stevens
  
  a+b+c>10
  
  (a+b+c) can be
  
  a b c
  
  1 2 8,9
  
  1 3 7,8,9
  
  1 4 6 ,7,8,9
  
  1 5 6,7,8,9
  
  1 6 7,8,9
  
  1 7 8,9
  
  1 8 9
  
  2 3 6,7,8,9
  
  2 4 5,6,7,8,9
  
  2 5 6,7,8,9
  
  2 6 7,8,9
  
  2 7 8,9
  
  2 8 9
  
  3 4 5,6,7,8,9
  
  3 5 6,7,8,9
  
  3 6 7,8,9
  
  3 7 8,9
  
  3 8 9
  
  4 5 6,7,8,9
  
  4 6 7,8,9
  
  4 7 8,9
  
  4 8 9
  
  5 6 7,8,9
  
  5 7 8,9
  
  5 8 9
  
  6 7 8,9
  
  6 8 9
  
  7 8 9
  
  Total 73 cases.
  
  ## Subscribe to Cheenta at Youtube
  
  Try this beautiful problem from the Pre-RMO, 2017 based on Sides of Quadrilateral.
  
  ## Sides of Quadrilateral - PRMO 2017
  
  What is the number of triples (a,b,c) of positive integers such that (i) a<b<c<10 and (ii) a,b,c,10 form the sides of a quadrilateral?
  
  • is 107
  • is 73
  • is 840
  • cannot be determined from the given information
  
  ### Key Concepts
  
  Largest number of triples
  
  Distance
  
  ## Check the Answer
  
  PRMO, 2017, Question 20
  
  Geometry Vol I to IV by Hall and Stevens
  
  a+b+c>10
  
  (a+b+c) can be
  
  a b c
  
  1 2 8,9
  
  1 3 7,8,9
  
  1 4 6 ,7,8,9
  
  1 5 6,7,8,9
  
  1 6 7,8,9
  
  1 7 8,9
  
  1 8 9
  
  2 3 6,7,8,9
  
  2 4 5,6,7,8,9
  
  2 5 6,7,8,9
  
  2 6 7,8,9
  
  2 7 8,9
  
  2 8 9
  
  3 4 5,6,7,8,9
  
  3 5 6,7,8,9
  
  3 6 7,8,9
  
  3 7 8,9
  
  3 8 9
  
  4 5 6,7,8,9
  
  4 6 7,8,9
  
  4 7 8,9
  
  4 8 9
  
  5 6 7,8,9
  
  5 7 8,9
  
  5 8 9
  
  6 7 8,9
  
  6 8 9
  
  7 8 9
  
  Total 73 cases.
  
  ## Subscribe to Cheenta at Youtube
  
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  ### Knowledge Partner
  
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explanation: The provided text is a detailed solution to a math problem from the Pre-Regional Mathematical Olympiad (PRMO) 2017. The problem asks for the number of triples \((a, b, c)\) of positive integers such that \(a < b < c < 10\) and \(a, b, c, 10\) form the sides of a quadrilateral. The solution lists all possible combinations of \((a, b, c)\) that satisfy the given conditions and concludes that there are 73 such triples.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: How Cheenta works to ensure student success?
  Explore the Back-Story
  
  # Sides of Quadrilateral | PRMO 2017 | Question 20
  
  Try this beautiful problem from the Pre-RMO, 2017 based on Sides of Quadrilateral.
  
  ## Sides of Quadrilateral - PRMO 2017
  
  What is the number of triples (a,b,c) of positive integers such that (i) a<b<c<10 and (ii) a,b,c,10 form the sides of a quadrilateral?
  
  • is 107
  • is 73
  • is 840
  • cannot be determined from the given information
  
  ### Key Concepts
  
  Largest number of triples
  
  Distance
  
  ## Check the Answer
  
  PRMO, 2017, Question 20
  
  Geometry Vol I to IV by Hall and Stevens
  
  a+b+c>10
  
  (a+b+c) can be
  
  a b c
  
  1 2 8,9
  
  1 3 7,8,9
  
  1 4 6 ,7,8,9
  
  1 5 6,7,8,9
  
  1 6 7,8,9
  
  1 7 8,9
  
  1 8 9
  
  2 3 6,7,8,9
  
  2 4 5,6,7,8,9
  
  2 5 6,7,8,9
  
  2 6 7,8,9
  
  2 7 8,9
  
  2 8 9
  
  3 4 5,6,7,8,9
  
  3 5 6,7,8,9
  
  3 6 7,8,9
  
  3 7 8,9
  
  3 8 9
  
  4 5 6,7,8,9
  
  4 6 7,8,9
  
  4 7 8,9
  
  4 8 9
  
  5 6 7,8,9
  
  5 7 8,9
  
  5 8 9
  
  6 7 8,9
  
  6 8 9
  
  7 8 9
  
  Total 73 cases.
  
  ## Subscribe to Cheenta at Youtube
  
  Try this beautiful problem from the Pre-RMO, 2017 based on Sides of Quadrilateral.
  
  ## Sides of Quadrilateral - PRMO 2017
  
  What is the number of triples (a,b,c) of positive integers such that (i) a<b<c<10 and (ii) a,b,c,10 form the sides of a quadrilateral?
  
  • is 107
  • is 73
  • is 840
  • cannot be determined from the given information
  
  ### Key Concepts
  
  Largest number of triples
  
  Distance
  
  ## Check the Answer
  
  PRMO, 2017, Question 20
  
  Geometry Vol I to IV by Hall and Stevens
  
  a+b+c>10
  
  (a+b+c) can be
  
  a b c
  
  1 2 8,9
  
  1 3 7,8,9
  
  1 4 6 ,7,8,9
  
  1 5 6,7,8,9
  
  1 6 7,8,9
  
  1 7 8,9
  
  1 8 9
  
  2 3 6,7,8,9
  
  2 4 5,6,7,8,9
  
  2 5 6,7,8,9
  
  2 6 7,8,9
  
  2 7 8,9
  
  2 8 9
  
  3 4 5,6,7,8,9
  
  3 5 6,7,8,9
  
  3 6 7,8,9
  
  3 7 8,9
  
  3 8 9
  
  4 5 6,7,8,9
  
  4 6 7,8,9
  
  4 7 8,9
  
  4 8 9
  
  5 6 7,8,9
  
  5 7 8,9
  
  5 8 9
  
  6 7 8,9
  
  6 8 9
  
  7 8 9
  
  Total 73 cases.
  
  ## Subscribe to Cheenta at Youtube
  
  This site uses Akismet to reduce spam. Learn how your comment data is processed.
  
  ### Knowledge Partner
  
  Cheenta is a knowledge partner of Aditya Birla Education Academy
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a detailed solution to a math problem from the Pre-Regional Mathematical Olympiad (PRMO) 2017. The problem asks for the number of triples \((a, b, c)\) of positive integers such that \(a < b < c < 10\) and \(a, b, c, 10\) form the sides of a quadrilateral. The solution lists all possible combinations of \((a, b, c)\) that satisfy the given conditions and concludes that there are 73 such triples.
  
  Label: question-and-answer