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How many triangles can be drawn by joining any three vertices of a pentagon?
(2013)
- a)8
- b)9
- c)11
- d)10
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
How many triangles can be drawn by joining any three vertices of a pen...
Required number of traingles = 
Here, n = number of items and
k = number you are picking at time
∴ n = 5, k = 3
Here, n = number of items and
k = number you are picking at time
∴ n = 5, k = 3
Community Answer
How many triangles can be drawn by joining any three vertices of a pen...
Number of Triangles in a Pentagon
There are a total of 5 vertices in a pentagon. To form a triangle, we need to select any 3 vertices out of these 5 vertices.
Calculating the Number of Triangles
- If we select 3 vertices that are not adjacent to each other, we can form 1 triangle.
- If we select 2 adjacent vertices and 1 non-adjacent vertex, we can form 2 triangles.
- If we select 2 non-adjacent vertices and 1 adjacent vertex, we can form 2 triangles.
- If we select 3 adjacent vertices, we can form 1 triangle.
Therefore, the total number of triangles that can be formed by joining any three vertices of a pentagon is 1 + 2 + 2 + 1 = 6.
Additional Triangles
However, we need to consider the triangles formed by the diagonals of the pentagon as well. Each diagonal forms a triangle with one side of the pentagon.
- There are 5 diagonals in a pentagon.
- Each diagonal forms 1 triangle with one side of the pentagon.
- Therefore, the number of additional triangles formed by the diagonals is 5.
Total Number of Triangles
Adding the triangles formed by selecting vertices and the triangles formed by the diagonals, we get a total of 6 + 5 = 11 triangles that can be drawn by joining any three vertices of a pentagon.
Therefore, the correct answer is option D) 11.
There are a total of 5 vertices in a pentagon. To form a triangle, we need to select any 3 vertices out of these 5 vertices.
Calculating the Number of Triangles
- If we select 3 vertices that are not adjacent to each other, we can form 1 triangle.
- If we select 2 adjacent vertices and 1 non-adjacent vertex, we can form 2 triangles.
- If we select 2 non-adjacent vertices and 1 adjacent vertex, we can form 2 triangles.
- If we select 3 adjacent vertices, we can form 1 triangle.
Therefore, the total number of triangles that can be formed by joining any three vertices of a pentagon is 1 + 2 + 2 + 1 = 6.
Additional Triangles
However, we need to consider the triangles formed by the diagonals of the pentagon as well. Each diagonal forms a triangle with one side of the pentagon.
- There are 5 diagonals in a pentagon.
- Each diagonal forms 1 triangle with one side of the pentagon.
- Therefore, the number of additional triangles formed by the diagonals is 5.
Total Number of Triangles
Adding the triangles formed by selecting vertices and the triangles formed by the diagonals, we get a total of 6 + 5 = 11 triangles that can be drawn by joining any three vertices of a pentagon.
Therefore, the correct answer is option D) 11.
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How many triangles can be drawn by joining any three vertices of a pentagon?(2013)a)8b)9c)11d)10Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many triangles can be drawn by joining any three vertices of a pentagon?(2013)a)8b)9c)11d)10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many triangles can be drawn by joining any three vertices of a pentagon?(2013)a)8b)9c)11d)10Correct answer is option 'D'. Can you explain this answer?.
How many triangles can be drawn by joining any three vertices of a pentagon?(2013)a)8b)9c)11d)10Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many triangles can be drawn by joining any three vertices of a pentagon?(2013)a)8b)9c)11d)10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many triangles can be drawn by joining any three vertices of a pentagon?(2013)a)8b)9c)11d)10Correct answer is option 'D'. Can you explain this answer?.
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