Your question is quite confusing because you used the phrase 'two polygon'. When asking mathematical or geometrical questions about shapes you ask about a single specific thing . I assume you meant to ask, '----number of sides of various different polygons, given the number of diagonals in each of them.' I have been drawing polygons with 5 and 6 and 7 and 8 sides and discovering the number of diagonals which can be drawn inside each of them , does not seem to follow a simple formula. I will look into it further and see if I can post you an answer in a day or two. Very interesting question I must say. Hope I can solve it .
Additional Information:-
The diagonal formula for any polygon is: 1/2*(n2-3n) = number of diagonals
Rearrange the formula into a quadratic equation and solve it for a positive value which will be the number of the sides of the given polygon
The five sided Polygon has 5 diagonals
The formula is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
A polygon with 14 diagonals will have 7 sides
209
1/2*(n2-3n) = number of diagonals Rearranging the formula: n2-3n-(2*diagonals) = 0 Solve as a quadratic equation and taking the positive value of n as the number of sides.
There is no such polygon that fits the given information.
A 7 sided polygon has 14 diagonals
The five sided Polygon has 5 diagonals
Number of diagonals = 1/2*(n2-3n) where n = the number of sides of the polygon.
Using the formula (x)(x-3)/2 = Diagonals ; simply replace the diagonals with the number of diagonals you're given. Then, you'll havev (x)(x-3)/2 = Diagonals. Simplify it, and you'll be given x(power of 2) - 3X = (2)(Diagonals). Subtract the amount of diagonals from both sides, and you'll have x(power of 2) - 3X - 2Diagonals = 0. From there, use the quadratic formula to find the number of sides the polygon has.
38 diagonals
It has 20 diagonals
It is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
The formula is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
A polygon with 14 diagonals will have 7 sides
11
209