Question

A polygon has 44 diagonals the number of its sides is

Answer 1

Answer:

11

Step-by-step explanation:

Using formula

no. of sides given by n and no. of diagonals are given by:-

nC2-n =44

n!/2!(n-2)! -n = 44

n(n-1)(n-2)!/2(n-2)! =44

n(n-1)/2 -n = 44

n(n-3)/2 =44

n(n-3) = 88

n²-3n-88 =0

n²-11n+8n -88 = 0

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

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

n = -8 is not possible

Hence n = 11

no. of sides are 11