Consider a convex polygon which has 44 diagonals then the number of triangles join
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Let the number of sides of polygon =n
∴∴ Number of angular points =n
∴∴ Number of straight lines joining any two of these n points =nC2nC2
Now the number of sides of the polygon =n
∴∴ Number of diagonals =nC2−nnC2−n
But it is given the number of diagonals=44
nC2−n=44nC2−n=44
n(n−1)2n(n−1)2−n=44−n=44
n2−n−2n=88n2−n−2n=88
n2−3n−88=0n2−3n−88=9
(n−11)(n+8)=0(n−11)(n+8)=0
n=11n=11 or n=−8n=−8
Rejecting negative quantity,
n=11n=11
Hence the required number of sides =11
hope it helps you
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