Q91 / 180 · COMEDK 2024 (Memory Based) · Mathematics
If a $n$-sided polygon has total 54 diagonal then the value of $n$ is
- A10
- B11
- Correct answerC12
- D13
Solution
$\because$ Number of diagonal in $n$-sided polygon
$\begin{array}{ll} <br/>& =\frac{n(n-3)}{2} \\<br/>\Rightarrow \quad & \frac{n(n-3)}{2}=54 \\<br/>& n^2-3 n=108 \\<br/>& n^2-3 n-108=0 \\<br/>\therefore \quad & n=12 \text { or } n=-9<br/>\end{array}$
$\begin{array}{ll} <br/>& =\frac{n(n-3)}{2} \\<br/>\Rightarrow \quad & \frac{n(n-3)}{2}=54 \\<br/>& n^2-3 n=108 \\<br/>& n^2-3 n-108=0 \\<br/>\therefore \quad & n=12 \text { or } n=-9<br/>\end{array}$
Hence, the correct answer is option: 'C'.