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A regular polygon with n sides has n(n-3)/2 diagonals. Find the number of sides of a regular polygon that has 44 diagonals.

Sagot :

konrad509

[tex]\dfrac{n(n-3)}{2}=44\\\\n(n-3)=88\\n^2-3n-88=0\\n^2+8n-11n-88=0\\n(n+8)-11(n+8)=0\\(n-11)(n+8)=0\\n=11 \vee n=-8[/tex]

Therefore, the number of sides is 11.

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