Question

76. Find the number of sides of a polygon whose number of diagonals is (i) 5 (ii) 14 (iii) 27 No. of diagonals n(n-3) 2.​

Answer 1

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We know that,

Number of diagonals of a polygon = 2n(n−3)

According to the question,

2n(n−3) = 27

n(n - 3) = 54 

n2 - 3n - 54 = 0

n2 9n + 6n - 54 = 0

n(n 9) + 6(n 9) = 0

(n + 6)(n - 9)=0

n = 9, - 6 (Neglecting negative value)

n = 9 

Hence, sides of polygon are 9.