Question

the number of diagonals that can be drawn in a opolygon of n sides is 1/2n(n-1)-n. If 230 diagonsaals can be drawn how many sides does the polygon have'

Answer 1

Answer:

n = 20

Step-by-step explanation:

The number of diagonal that can be drawn in a polygon of n sides is given by :

$D=\dfrac{n(n-3)}{2}$

If the number of diagonals are 230, then put D = 230 in above formula. So,

$230=\dfrac{n(n-3)}{2}\\\\460=n^2-3n\\\\n^2-3n-460=0$

It is a quadratic equation, the value of n is equal to 20.

It means that for 230 diagonal, there are 20 sides of the polygon.