SOLUTION: An n-sided polygon has
(n(n - 3))/2 diagonals. a How many sides has a polygon with 665 diagonals? b Why can’t a polygon have 406 diagonals?
Algebra.Com
Question 1086341: An n-sided polygon has
(n(n - 3))/2 diagonals. a How many sides has a polygon with 665 diagonals? b Why can’t a polygon have 406 diagonals?
Found 2 solutions by MathLover1, htmentor:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
An n-sided polygon has
diagonals
if a polygon has diagonals, we have
...factor
solutions:
=>
=>=> disregard negative solution if looking for number of the sides
b. Why can’t a polygon have diagonals?
}
}
}
}...can't be factored, so use quadratic formula
solutions: use positive only
=> decimal number cannot be solution to number of sides, it have to be an integer because a polygon has integer number of sides
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Number of diagonals = d = (n/2)(n-3) -> n^2 - 3n - 2d = 0
a) Solve for n, when d = 665
n^2 - 3n - 1330 = 0
This can be factored as (n-38)(n+35) = 0
We take the positive solution, n = 38
For d = 406, we have the equation n^2 - 3n - 812 = 0
This does not give an integer solution for n. Thus no polygon can have 406 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 polygons of n sides has 1/2n(n-3) diagonals, how many sides will a polygon with 65... (answered by MathLover1)
If a polygonal n sides has (n/2)(n - 3) diagonals, how many sides will a polygon with 65... (answered by ikleyn,math_tutor2020)
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)
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)
the number of diagonals d of a polygon of n sides is given by d = n/2 (n-3). How many... (answered by ikleyn,Alan3354)
no.of diagonals a polygon having 'n' sides has 1\2n(n-3) . is there a polygon with 25... (answered by robertb)