Question

The number of diagonals in a polygon, d_(r) in terms of the number of sides of a polygon, n_(r) is given by the equation d=(n(n-3))/(2) What equation shows the number of sides of a polygon in terms of the number of diagonals?

Answer 1

Answer and Step-by-step explanation:

To find the equation that shows the number of sides of a polygon in terms of the number of diagonals, we can rearrange the given equation that relates the number of diagonals to the number of sides of a polygon.

The given equation is:

d = (n(n-3))/2

To find the equation for the number of sides in terms of the number of diagonals, we can rearrange the equation to isolate n (the number of sides).

1. Multiply both sides of the equation by 2:

2d = n(n-3)

2. Expand the equation:

2d = n^2 - 3n

3. Rearrange the equation:

n^2 - 3n - 2d = 0

Therefore, the equation that shows the number of sides of a polygon in terms of the number of diagonals is:

n^2 - 3n - 2d = 0