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How many sides does a polygon having 27 diagonals have? 5 6 7 8
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05 Jan 2025, 22:54
05 Jan 2025, 22:54
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How many sides does a polygon having 27 diagonals have?
A, 5
B. 6
C. 7
D. 8
E. 9
A, 5
B. 6
C. 7
D. 8
E. 9
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Re: How many sides does a polygon having 27 diagonals have? 5 6 7 8
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17 Feb 2025, 02:32
17 Feb 2025, 02:32
Expert Reply
OFFICIAL EXPLANATION
The number of diagonals in an $n$ sided polygon is $\(\frac{n(n-3)}{2}\)$
Let the number of sides of a polygon having 27 diagonals be $\(k\)$, so we get $\(\frac{k(k-3)}{2}=27\)$ i.e. $\(\mathrm{k}(\mathrm{k}-3)=54=9 \times(9-3)\)$ so it is true for $\(\mathrm{k}=9\)$
Hence the polygon having 27 diagonals must have 9 sides, so the answer is $\((E)\)$.
The number of diagonals in an $n$ sided polygon is $\(\frac{n(n-3)}{2}\)$
Let the number of sides of a polygon having 27 diagonals be $\(k\)$, so we get $\(\frac{k(k-3)}{2}=27\)$ i.e. $\(\mathrm{k}(\mathrm{k}-3)=54=9 \times(9-3)\)$ so it is true for $\(\mathrm{k}=9\)$
Hence the polygon having 27 diagonals must have 9 sides, so the answer is $\((E)\)$.
gmatclubot
Re: How many sides does a polygon having 27 diagonals have? 5 6 7 8 [#permalink]
17 Feb 2025, 02:32
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