+1242
The number of diagonals in a certain regular polygon is equal to five times the number of sides. How many sides does this polygon have?
+128473 The number of diagonals in a regular polygon of n sides = n(n - 3) / 2
So
n(n - 3) / 2 = 5n multiply boh sides by 2
n(n -3) = 10n simplify
n^2 - 3n = 10n subtract 10n from both sides
n^2 - 13n = 0 factor
n ( n - 13) = 0
Set each factor to 0 and solve for n and we get
n= 0 [ reject] or n = 13
So....13 sides
