COMEDK · Maths · 4. Permutation Combination
If a polygon of \(n\) sides has 275 diagonals, then \(n\) is equal to
- A 25
- B 35
- C 20
- D 15
Answer & Solution
Correct Answer
(A) 25
Step-by-step Solution
Detailed explanation
The number of diagonals in a polygon of \(n\) sides is given by the formula \(D = \dfrac{n(n - 3)}{2}\). Given \(D = 275\), we have the equation: \(\dfrac{n(n - 3)}{2} = 275\) \(n(n - 3) = 550\) \(n^2 - 3n - 550 = 0\) Solving the quadratic equation using the quadratic formula…
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