Diagonals

Geometry Level 2

A convex polygon has 44 diagonals. The number of its sides is :


The answer is 11.

Sakanksha Deo by Sakanksha Deo , 23, India

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1 solution

Sakanksha Deo
Mar 12, 2015

Number of diagonals = n ( n − 3 ) 2 \frac{ n ( n - 3 ) }{2} ( where n = number of sides )

→ 88 = n 2 − 3 n \rightarrow 88 = n^2 - 3n

Solving the equation,we get,

n = -8 , 11

Since number of sides cannot be negative,

So,

n = number of sides = 11 \boxed{11}

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http://www.mathopenref.com/polygondiagonal.html

Sathvik Acharya - 4 years, 2 months ago

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