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Polygon

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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
+2222
+1

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
+124509
+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

Jun 24, 2022