SOLUTION: What is the name of a polygon if the number of its diagonals is 10 times the number of sides? show solution

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Question 1186813: What is the name of a polygon if the number of its diagonals is 10 times the number of sides? show solution
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


If n is the number of sides of the polygon, then the number of diagonals is

%28n%28n-3%29%29%2F2

The given condition is then this:

%28n%28n-3%29%29%2F2=10n
%28n%5E2-3n%29%2F2=10n
n%5E2-3n=20n
n%5E2-23n=0
n%28n-23%29=0

n=0 or n=23; obviously n=0 makes no sense, so n=23

The polygon has 23 sides.

For the NAME of that polygon, you can do an internet search....