Question 943814

A regular polygon has 6 times as many diagonals as sides. How many sides does this polygon
have? How do you solve it,whats the strategy?
<pre>No special strategy!! Just the use of the formula.
Formula for determining the number of diagonals of a polygon: {{{n(n - 3)/2}}}, with n being the number of sides
Since there are 6 times as many diagonals as numbers of sides, then number of diagonals = 6n
We now have: {{{n(n - 3)/2 = 6n}}}
{{{(n^2 - 3n)/2 = 6n}}}
{{{n^2 - 3n = 12n}}} ------ Cross-multiplying
{{{n^2 - 3n - 12n = 0}}}
{{{n^2 - 15n = 0}}}
n(n - 15) = 0
Number of sides, or {{{highlight_green(n = 15)}}}       OR       n = 0 (ignore)