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  • A convex polygon has 44 diagonals. Find the number of its sides. [Hint: Polygon of n sides has (nC2 - n) number of diagonals.]

A convex polygon has 44 diagonals. Find the number of its sides. [Hint: Polygon of n sides has (^nC_2 - n) number of diagonals.]

Answers (1)

Let the convex polygon have n sides.

 Number of diagonals = number of ways of selecting two vertices- number of sides

\\n_{c_{2}}-n=44 \\\\ \frac{n !}{2 !(n-2) !}-n=44 \\\\ \frac{n(n-1)}{2}-n=44 \\\\ n(n-1)-2 n=88 \\\\ n^{2}-3 n-88=0 \\\\ (n-11)(n+8) \\\\ n=11

 

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