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Question
A polygon has 44 diagonals. Then number of its sides is
A polygon has 44 diagonals. Then number of its sides is
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Solution
The correct option is B 11
Let the polygon has n sides.No, of line segments obtained by joining vertices=NC2Our of these n lilne aegments are sides are sides of the polygon.So.No. of diagonals of the polygon =nC2−nGiven, nC2−n=44n(n−1)2−n=44n(n−3)2=44n2−3n−88=0(n−11)(n+8)=0n=11orn=−8Since,n cannot be negative n=11The polygon has 11 sides.
Let the polygon has n sides.
No, of line segments obtained by joining vertices=NC2
Our of these n lilne aegments are sides are sides of the polygon.
So.
No. of diagonals of the polygon =nC2−n
Given, nC2−n=44
n(n−1)2−n=44n(n−3)2=44n2−3n−88=0(n−11)(n+8)=0n=11orn=−8
Since,
n cannot be negative n=11
The polygon has 11 sides.
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