SOLUTION: how many diagonals are there in 23 sides? how many diagonals are there in 80 sides? how many sides are there in 135 diagonals? how many sides are there in 152 diagonals? how ma

Algebra ->  Polygons -> SOLUTION: how many diagonals are there in 23 sides? how many diagonals are there in 80 sides? how many sides are there in 135 diagonals? how many sides are there in 152 diagonals? how ma      Log On


   

Question 626627: how many diagonals are there in 23 sides?
how many diagonals are there in 80 sides?
how many sides are there in 135 diagonals?
how many sides are there in 152 diagonals?
how many sides are there in 275 diagonals?
how many sides are there in 350 diagonals?
how many sides are there in 1377 diagonals?
- thanks. :)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Note:  D+=+n%28n-3%29%2F2

how many diagonals are there in 80 sides? D+=+80%2880-3%29%2F2

how many sides are there in 152 diagonals?

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

   304 = n^2 - 3n

     n^2 - 3n - 304 = 0

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

n+=+%283+%2B-+sqrt%28+1225%29%29%2F%282%29+

 n+=+%283+%2B-+35%29%2F%282%29+

    n = 19   (tossing out negative solution for n)