Combinations
The number of diagonals in a polygon with n sides is
Select the correct option:
Solution
n(n-3)/2
- Total Segments: A polygon with n vertices allows (2n) total ways to join any two vertices.
- Total Segments =2n(n−1).
- Filter Segments: These segments consist of either sides or diagonals.
- Subtract Sides: There are n sides in an n-sided polygon.
- Diagonals =2n(n−1)−n.
- Simplification:
- 2n2−n−2n=2n2−3n=2n(n−3).
- Example: A square (n=4) has 24(4−3)=2 diagonals.
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About This Question
- Subject
- mathematics
- Chapter
- permutations and combinations
- Topic
- combinations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
n(n-3)/2
- Total Segments: A polygon with n vertices allows (2n) total ways to join any two vertices.
- Total Segments =2n(n−1).
- Filter Segments: These segments consist of either sides or diagonals.
- Subtract Sides: There are n sides in an n-sided polygon.
- Diagonals =2n(n−1)−n.
- Simplification:
- 2n2−n−2n=2n2−3n=2n(n−3).
- Example: A square (n=4) has 24(4−3)=2 diagonals.
This medium difficulty mathematics question is from the chapter permutations and combinations, covering the topic of combinations. It appeared in the 2025 exam.
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