Question

A polygon has 44 diagonals. The number of the sides is
(a) 10
(b) 11
(c) 12
(d) 13
​

Answer 1

Answer: C) 11

Explanation:

Let the number of sides be n.

The number of diagonals is given by nC2 - n

Therefore, nC2 - n = 44, n>0

nC2 - n = 44

n2 - 3n - 88 = 0

n2 -11n + 8n - 88 = 0

n(n - 11) + 8(n - 11) = 0

n = -8 or n = 11.

As n>0, n will not be -8. Therefore, n=11.

Answer 2

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❤$\pink {ANSWER\:(C)11}$❤

Explanation:

• Let the number of sides be n.

• The number of diagonals is given by nC2 - n

• Therefore, nC2 - n = 44, n>0

• nC2 - n = 44

• n2 - 3n - 88 = 0

• n2 -11n + 8n - 88 = 0

• n(n - 11) + 8(n - 11) = 0

• n = -8 or n = 11.

• As n>0, n will not be -8. Therefore, n=11.

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