If a polygon of ‘n’ sides has 1/2 n (n−3) diagonals. How many sides will a polygon having 65 diagonals? Is there a polygon with 50 diagonals?
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Answered by
57
1/2 n (n−3)=65
n^2-3n=130
n^2-3n-130=0
(n-13)(n+10)=0
n=13,-10
no. of sides=13
1/2 n (n−3)=50
n^2-3n-100=0
n=3+_sqrt(409)/2
which will not give any positive integral value
as n is no. of sides, there is no polygon with 50 diagonals
n^2-3n=130
n^2-3n-130=0
(n-13)(n+10)=0
n=13,-10
no. of sides=13
1/2 n (n−3)=50
n^2-3n-100=0
n=3+_sqrt(409)/2
which will not give any positive integral value
as n is no. of sides, there is no polygon with 50 diagonals
Answered by
39
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