Question 1210521
.
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?
~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let n be the number of sides.

The number of diagonals is then  {{{(n*(n-3))/2}}}.


From the problem, we have this equation

    {{{(n*(n-3))/2}}} = 2n.


It implies

    {{{(n-3)/2}}} = 2,

    n-3 = 4,

     n = 4 + 3 = 7.


<U>ANSWER</U>.  The number of sides is 7.


<U>CHECK</U>.  The number of diagonals is  {{{(7*(7-3))/2}}} = {{{(7*4)/2}}} = 7*2 = 14.   ! correct !
</pre>

Solved.