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