Question

If a polygon of n sides has 1/2 n(n-3)diagonals.how many sides are there in a polygon with 65 diagonals? Is there a polygon with 50 diagonals?

Answer 1

Answer:

no

Step-by-step explanation:

n(n-3)/2=65

n(n-3)=130

n^2-3n-130=0

factorize the equation

n(n-13)+10(n-13)=0

(n+10)n-13=0

n=-10or 13

the polygon with 65 diagonals have 13 sides

n(n-3)/2=50

n^2-3n-100=0

if we factorize this equation we won't get positive integers coz the sides can't be in negative nos. so we can conclude that there is no polygon with 50 diagonals