+810 The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides. How many sides does this polygon have?
+3198
The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides.
How many sides does this polygon have?
Using the formula for the number of diagonals D of a polygon with n sides
n (n – 3)
D = ––––––––
2
and it's given that D = 2 n, therefore
n (n – 3)
2 n = –––––––– ==>> 4n = n2 – 3n ==>> n2 – 7n = 0
2 n (n – 7) = 0
n = 0
n = 7
.
