SOLUTION: if polygons of n sides has 1/2n(n-3) diagonals, how many sides will a polygon with 65 diagonals have? is there a ploygon 80 diagonal
Algebra.Com
Question 750743: if polygons of n sides has 1/2n(n-3) diagonals, how many sides will a polygon with 65 diagonals have? is there a ploygon 80 diagonal
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Let be the number of sides = number of vertices.
Then can be connected to other vertices, giving connections. However, this counts each vertex pair connection twice, so there are:
diagonals.
Thus if there are diagonals:
...write as
...group
so or
As a polygon cannot have a negative number of sides, .
if there are diagonals:
...use quadratic formula
solutions:
so, since and is equal to the number of sides, means that a polygon cannot have a number of sides as decimal number
there is a polygon with diagonals
RELATED QUESTIONS
If a polygon of n sides has (n/2)(n - 3) diagonals, how many sides will a polygon with 65 (answered by ikleyn)
Solve the problem.
If a polygon, of n sides has 1/2n(n - 3) diagonals, how many sides... (answered by Edwin McCravy)
If a polygon of n sides has (1/2)(n)(n - 3) diagonals, how many sides will a polygon with (answered by ikleyn,math_tutor2020)
If a polygonal n sides has (n/2)(n - 3) diagonals, how many sides will a polygon with 65... (answered by ikleyn,math_tutor2020)
no.of diagonals a polygon having 'n' sides has 1\2n(n-3) . is there a polygon with 25... (answered by robertb)
In geometry, a convex polygon is a many-sided closed figure, with no sides collapsing in... (answered by ikleyn)
The number of diagonals d in a polygon with n sides is given by the formula d=n^2-3n/2.... (answered by HyperBrain)
An n-sided polygon has
(n(n - 3))/2 diagonals. a How many sides has a polygon with 665 (answered by MathLover1,htmentor)
Polygon K has 3 more sides and 2015 more diagonals than polygon N. How many sides does... (answered by ikleyn)