Diagonals

What x-gon has 54 diagonals?

Final Answer:

x =  12

Step-by-step explanation:

54 = 2n(n3)  54 2=n(n3)  54 2=n(n3) n2+3n+108=0 n23n108=0  a=1;b=3;c=108 D=b24ac=3241(108)=441 D>0  n1,2=2ab±D=23±441 n1,2=23±21 n1,2=1.5±10.5 n1=12 n2=9  x>0  x=n1=12

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