First slide

Combinations

Question

If a polygon has 14 diagonals, then the number of its sides are

Moderate

A

11
B

7
C

8
D

None of these

Solution

Let n be the number of diagonals of a polygon .Then
$\begin{array}{l} ^{n} C_{2} - n = 44 \\ \Rightarrow \frac{n (n - 1)}{2} - n = 44 \\ \Rightarrow n^{2} - 3 n - 88 = 0 \\ \Rightarrow n = - 8 or 11 \\ n = 11 \end{array}$

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