Question:
If in a regular polygon the number of diagonals is $54$, then the number of sides of this polygon is :
If in a regular polygon the number of diagonals is $54$, then the number of sides of this polygon is :
Updated On: Sep 30, 2024
- 10
- 12
- 9
- 6
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The Correct Option is B
Solution and Explanation
Number of diagonal $= 54$
$\Rightarrow \frac{n\left(n-3\right)}{2}=54$
$\Rightarrow n^{2}-3n-108=0$
$\Rightarrow n^{2}-12n+9n-108 =0$
$\Rightarrow n\left(n- 12\right)+9\left(n-12\right) = 0$
$\Rightarrow n=12,-9$
$\Rightarrow n=12 \left(\because n\ne-9\right)$
$\Rightarrow \frac{n\left(n-3\right)}{2}=54$
$\Rightarrow n^{2}-3n-108=0$
$\Rightarrow n^{2}-12n+9n-108 =0$
$\Rightarrow n\left(n- 12\right)+9\left(n-12\right) = 0$
$\Rightarrow n=12,-9$
$\Rightarrow n=12 \left(\because n\ne-9\right)$
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