SOLUTION: the number of diagonal of a regular polygon is779.find how many side it has

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Question 1005637: the number of diagonal of a regular polygon is779.find how many side it has


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
d = number of diagonals
n = number of sides

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In this case,
d = 779
n = unknown (we're solving for this)

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We will use the formula d+=+%28n%28n-3%29%29%2F2
Plug in d+=+779 and solve for n

d+=+%28n%28n-3%29%29%2F2

779+=+%28n%28n-3%29%29%2F2

779%2A2+=+2%2A%28%28n%28n-3%29%29%2F2%29 Multiply both sides by 2

1558+=+n%28n-3%29

1558+=+n%5E2-3n

1558-1558+=+n%5E2-3n-1558 Subtract 1558 from both sides

0+=+n%5E2-3n-1558

n%5E2-3n-1558+=+0

Use the quadratic formula to find that n=41 or n=-38.

Ignore n=-38 since it doesn't make sense to have a negative number of diagonals.

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The only solution is n=41

There are 41 sides.