The number of diagonals in a certain regular polygon is equal to \(6\) times the number of sides. How many sides does this polygon have?
+2668 The formula for diagonals is: \(s(s-3) \over2\)
We now have an equation to solve: \({s(s-3) \over 2} = 6s\)
Simplifying: \(s^2-3s=12s\)
Converting to a quadratic, we get: \(s^2 - 15s = 0\)
We know that \(15s = s^2\), so there are \(\color{brown}\boxed {15}\) sides.
+2668 The formula for diagonals is: \(s(s-3) \over2\)
We now have an equation to solve: \({s(s-3) \over 2} = 6s\)
Simplifying: \(s^2-3s=12s\)
Converting to a quadratic, we get: \(s^2 - 15s = 0\)
We know that \(15s = s^2\), so there are \(\color{brown}\boxed {15}\) sides.
