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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?

 

There was a question similar to this except it was 5 times the number of sides, please help me.

 

Thanks!

 Jan 12, 2020
 #1
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The polygon will have 14 sides.

 Jan 12, 2020
 #2
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sry incorrect

Guest Jan 12, 2020
 #3
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The formula for the number of diagonals of a polygon is:  n(n - 3) / 2         (where n is the number of sides)

 

So, the equation is;               n(n - 3)/2  =  4n

Multiplying both sides by 2:      n(n - 3)  =  8n

Solving:                                     n2 - 3n  =  8n

                                                 n2 - 11n  =  0

                                                 n(n - 11)  =  0

 

Since a polygon can't have 0 sides; the answer is:  11 sides

 Jan 12, 2020

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