A polygon has 44 diagonals. The number of its sides are

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Solution

Q.
A polygon has 44 diagonals. The number of its sides are

1 9

2 8

3 11

4 7

Ans.
(3)

$Number of sides = n$

$Number of vertices = n$

$Number of diagonals = {}^{n}C_{2} - n$

$\Rightarrow$ $44 = {}^{n}C_{2} - n \Rightarrow \frac{n (n - 1)}{2} - n = 44$

$\Rightarrow$ $n^{2} - 3 n - 88 = 0$

$∴$ $n = 11$ $(∵ n cannot be negative)$

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