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The number of diagonals in a certain regular polygon is equal to five times the number of sides. How many sides does this polygon have?

 Dec 1, 2018
 #1
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See the answer here: https://web2.0calc.com/questions/geometry_74984

 Dec 1, 2018
 #2
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The number of diagonals in a regular polygon of n sides = n(n - 3) / 2

 

So

 

n(n - 3) / 2 =  5n     multiply boh sides by 2

 

n(n -3) = 10n       simplify

 

n^2 - 3n = 10n     subtract 10n from both sides

 

n^2 - 13n = 0      factor

 

n ( n - 13) = 0

 

Set each factor to 0 and solve for n and we get

 

n= 0   [ reject]    or        n = 13

 

So....13 sides

 

 

cool cool cool

 Dec 1, 2018

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