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

 May 10, 2020
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Find the number of sides in a regular polygon in which the number of diagonals is equal to four times the number of sides.

 

Formula for he number of diagonals in a polygon:  n(n-3)/2

Since the number of diagonals is four times the numbe of sides:  n(n - 3)/2  =  4n

-- cross-multiplying:  n(n - 3)  =  8n

                                  n2 - 3n  =  8n

                                 n2 - 11n  =  0

                                 n(n - 11)  =  0

So, either  n = 0 (impossible) or  n = 11.

 May 10, 2020

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