Polygon question?

Question

Find the number of sides of a polygon having 9 diagonals.

this is the formula: n(n-3)/2

could you please solve this for me and explain it good...

Answer 1

i think its 27

Answer 2

Got it!

9=n(n-3)/2

9=(n^2-3n)/2 (distribute)

18=n^2-3n (multiply both sides by 2)

0=n^2-3n-18 (move the 18 over)

0=(n-6)(n+3) (factor out)

n=6 or n=-3 (find what n can equal)

Now, since we are trying to find the number of sides, it can't be negative therefore our answer is 6.

Answer 3

It's a hexagon. It's the only polygon that has 9 diagonals. Sadly, I don't know how to explain the formula. Sorry.