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

 Jun 24, 2022
 #1
avatar+2448 
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The formula for the number of diagonals in a polygon is \(s(s-3) \div 2\), where s is the numberof sides. 

 

Setting this equal to 2s, we have: \({s(s-3) \over 2} = 2s\)

 

Solving, we find s = 0 or 7. 

 

But, s can't be 0, so \(s = \color{brown}\boxed{7}\)

 Jun 24, 2022
 #2
avatar+124676 
+2

The equation for the  number of  diagonals in a  regular polygon is

 

n ( n - 3) / 2      where n is the number of  sides

 

So we have

 

n (n -3)  / 2  =  2n

 

n ( n - 3) = 4n

 

n^2 - 3n  = 4n

 

n^2 - 7n =  0

 

n ( n - 7)  = 0

 

The second factor gives us what we need

 

n - 7 = 0

 

n = 7

 

 

cool cool cool

 Jun 24, 2022

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