Q83 / 180 · COMEDK 2023 (Morning Shift) · Mathematics
A polygon of n sides has 90 diagonals, then n is equal to
- A20
- B$-$14
- C21
- Correct answerD15
Solution
The formula for number of diagonals in a polygon of $n$ sides is $D = \dfrac{n(n-3)}{2}$
Setting $D = 90$:
$\dfrac{n(n-3)}{2} = 90$
$n^2 - 3n - 180 = 0$
$(n-15)(n+12) = 0$
$n = 15$ or $n = -12$
Since $n$ must be a positive integer, $n = 15$.
Setting $D = 90$:
$\dfrac{n(n-3)}{2} = 90$
$n^2 - 3n - 180 = 0$
$(n-15)(n+12) = 0$
$n = 15$ or $n = -12$
Since $n$ must be a positive integer, $n = 15$.
Hence, the correct answer is option: 'D'.