SOLUTION: If a regular polygon has a total of nine diagonals, how many sides does it have?

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Question 698952: If a regular polygon has a total of nine diagonals, how many sides does it have?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The formula for the number of diagonals in a polygon with n sides is:
n%28n+-3%29%2F2=d
Now solve this for d=9 diagonals:
n%28n+-3%29%2F2=9
n%28n+-3%29=9%2A2
n%5E2-3n=18
n%5E2-3n-18=0.....use quadratic formula

n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

n+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A%28-18%29+%29%29%2F%282%2A1%29+

n+=+%283+%2B-+sqrt%28+9%2B72%29%29%2F2+

n+=+%283+%2B-+sqrt%2881%29%29%2F2+
n+=+%283+%2B-+9%29%2F2+..we will need only positive solution
n+=+%283+%2B9%29%2F2+
n+=+12%2F2+
n+=+6

So the number of sides is 6.