The no. of sides in a polygon with 27 diagonals is :
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diagonal=n(n-3)/2
∴27=n(n-3)/2
⇒n(n-3)=27*2
⇒n²=3n=54
⇒n²-3n-54=0
⇒n²-9n+6n-54=0
⇒n(n-9)+6(n-9)=0
⇒(n-9)(n+6)
∴n=9 (we can't take -6 as polynomail is always positive)
∴n=9
∴27=n(n-3)/2
⇒n(n-3)=27*2
⇒n²=3n=54
⇒n²-3n-54=0
⇒n²-9n+6n-54=0
⇒n(n-9)+6(n-9)=0
⇒(n-9)(n+6)
∴n=9 (we can't take -6 as polynomail is always positive)
∴n=9
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