SOLUTION: A convex polygon is a polygon whose interior angles are between 0 and 180. The number of diagonals D in a convex polygon with n sides is given by the formula D=1/2n (n-3). Determin

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A convex polygon is a polygon whose interior angles are between 0 and 180. The number of diagonals D in a convex polygon with n sides is given by the formula D=1/2n (n-3). Determin      Log On


   

Question 1033105: A convex polygon is a polygon whose interior angles are between 0 and 180. The number of diagonals D in a convex polygon with n sides is given by the formula D=1/2n (n-3). Determine the number of sides n in a convex polygon that has 27 diagonals by solving the equation 27=1/2n(n-3)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
D+=+%28n%28n-3%29%29%2F2 ==> 27+=+%28n%28n-3%29%29%2F2 ==> 54+=+n%5E2+-+3n
==> n%5E2+-+3n+-+54+=+0 ==> (n-9)(n+6) = 0 ==> n = 9. (n = -6 is not acceptable.)
Therefore the convex polygon has 9 sides.